Graphing and Solving for Zeros
•
0 likes•177 views
This document discusses graphing functions and finding their zeros. It reviews linear functions like y=x+3 and quadratic functions like f(x)=x^2. It shows examples of graphing these functions and finding their y-intercepts and x-intercepts, particularly focusing on finding the values of x where the function equals 0, known as the zeros.
Report
Share
Report
Share
Download to read offline
Recommended
8th alg -l3.1--oct29
This document contains notes from a math lesson on linear equations. It includes examples of evaluating expressions, solving equations, defining key terms like standard form and intercepts. It also shows how to graph linear equations by finding intercepts or making a table of values. Students are assigned problems #7-11 and #24-34 evens from pages 157-158 for homework due on October 31st.
Factoring trinomials lc1
The document outlines notes from a math class on factoring trinomials. It includes the objective to factor trinomials, an agenda of topics to cover, examples of factoring various trinomials like x^2 + 5x + 6 and z^2 - 14z - 15. It also covers factoring perfect square trinomials using the formula a^2 + 2ab + b^2 = (a + b)^2 and examples like x^2 + 14x + 49 and 4y^2 - 12y + 9.
Quatitative Analysis
This document contains two math questions. The first question defines the change in Z to be equal to H, and defines the function F(x) as x to the sixth power divided by 6 plus 2x cubed. The second question does not provide any details.
Quadratic Function by Taylor & Asia
Quadratic functions are functions that can be described by an equation in the form f(x)=ax^2+bx+c. Examples of quadratic functions include f(x) = -2x^2 + x - 1 and f(x) = x^2 + 3x + 2. Quadratic equations were used to describe the orbits of planets around the sun and allow observation of planetary motion. Structural engineers also use quadratic equations to design tall skyscrapers.
Integration worksheet.
This document provides a tutorial on topics related to calculus including:
1) Differentiating various functions and finding points where the gradient is zero
2) Evaluating definite integrals of functions including trigonometric, exponential, and rational functions
3) Finding areas bounded by curves, axes, and lines by evaluating definite integrals
4) Sketching graphs of functions and finding relevant information like minimum/maximum points
5) Finding equations of tangents and normals to curves at given points
Fungsi kuadrat
The function F(x) = 2x + 3 is a linear function that increases at a rate of 2 units for every 1 unit increase in x, with a y-intercept of 3. The function f(x) = x^2 + 2x - 3 is a quadratic function that is symmetric around the y-axis, with its vertex at the point (-1,0) and intersecting the x-axis at x = -3 and x = 0.
8
The functions f(x) = 3x^2 + 17x - 6 and g(x) = -x + 6 are given. To find (f + g)(x), add the corresponding terms of f(x) and g(x) to obtain (f + g)(x) = 3x^2 + 16x.
7th pre alg -l27--oct16
The document discusses laws of exponents and their applications. It introduces the laws that na x nb = na+b, na / nb = na-b, and (na)b = na x b. It also notes that anything to the power of zero equals one. The document then provides examples of using these laws to find missing exponents, simplify expressions, and write expressions as powers of 10.
Recommended
8th alg -l3.1--oct29
This document contains notes from a math lesson on linear equations. It includes examples of evaluating expressions, solving equations, defining key terms like standard form and intercepts. It also shows how to graph linear equations by finding intercepts or making a table of values. Students are assigned problems #7-11 and #24-34 evens from pages 157-158 for homework due on October 31st.
Factoring trinomials lc1
The document outlines notes from a math class on factoring trinomials. It includes the objective to factor trinomials, an agenda of topics to cover, examples of factoring various trinomials like x^2 + 5x + 6 and z^2 - 14z - 15. It also covers factoring perfect square trinomials using the formula a^2 + 2ab + b^2 = (a + b)^2 and examples like x^2 + 14x + 49 and 4y^2 - 12y + 9.
Quatitative Analysis
This document contains two math questions. The first question defines the change in Z to be equal to H, and defines the function F(x) as x to the sixth power divided by 6 plus 2x cubed. The second question does not provide any details.
Quadratic Function by Taylor & Asia
Quadratic functions are functions that can be described by an equation in the form f(x)=ax^2+bx+c. Examples of quadratic functions include f(x) = -2x^2 + x - 1 and f(x) = x^2 + 3x + 2. Quadratic equations were used to describe the orbits of planets around the sun and allow observation of planetary motion. Structural engineers also use quadratic equations to design tall skyscrapers.
Integration worksheet.
This document provides a tutorial on topics related to calculus including:
1) Differentiating various functions and finding points where the gradient is zero
2) Evaluating definite integrals of functions including trigonometric, exponential, and rational functions
3) Finding areas bounded by curves, axes, and lines by evaluating definite integrals
4) Sketching graphs of functions and finding relevant information like minimum/maximum points
5) Finding equations of tangents and normals to curves at given points
Fungsi kuadrat
The function F(x) = 2x + 3 is a linear function that increases at a rate of 2 units for every 1 unit increase in x, with a y-intercept of 3. The function f(x) = x^2 + 2x - 3 is a quadratic function that is symmetric around the y-axis, with its vertex at the point (-1,0) and intersecting the x-axis at x = -3 and x = 0.
8
The functions f(x) = 3x^2 + 17x - 6 and g(x) = -x + 6 are given. To find (f + g)(x), add the corresponding terms of f(x) and g(x) to obtain (f + g)(x) = 3x^2 + 16x.
7th pre alg -l27--oct16
The document discusses laws of exponents and their applications. It introduces the laws that na x nb = na+b, na / nb = na-b, and (na)b = na x b. It also notes that anything to the power of zero equals one. The document then provides examples of using these laws to find missing exponents, simplify expressions, and write expressions as powers of 10.
Truth, deduction, computation lecture f
This document contains a lecture on functions, λ-calculus, and Peano arithmetic. It defines functions, injections, surjections, bijections, function composition, and identity functions. It introduces λ-calculus, including β-reduction and shows how Church numerals can represent numbers. It then covers Peano arithmetic, defining numbers, addition, multiplication, and exponentiation recursively using λ-terms.
8th Alg - L8.4--March26
This document contains an assignment and lesson on factoring polynomials and solving equations. [1] The assignment is to complete odd problems 2-28 from page 496 in the textbook and Checkpoints 8.1-8.3 by Wednesday. [2] The lesson explains how to factor trinomials that do not have a leading coefficient of 1 by finding two integers whose sum is the coefficient of the x-term and whose product is the constant term. [3] It provides examples of factoring various polynomials and solving equations, checking solutions.
Chapter 16
This document contains a chapter on topics in vector calculus, including exercises on vector fields, divergence, curl, and applications of vector calculus identities and theorems. The exercises involve calculating divergence and curl of various vector fields, applying vector calculus operations like divergence and curl to scalar and vector functions, and manipulating vector calculus identities.
Simultaneous eqn2
1) Simultaneous equations involve two variables in two equations that are solved simultaneously to find the values of the variables.
2) To solve simultaneous equations, one first expresses one variable in terms of the other by changing the subject of one linear equation, then substitutes this into the other equation to obtain a quadratic equation.
3) This quadratic equation is then solved using factorisation or the quadratic formula to find the values of the variables that satisfy both original equations.
Lesson5 Oct14
This document provides steps for sketching the graphs of absolute value functions: sketch the underlying function first, then reflect any parts below the x-axis over the x-axis to obtain the absolute value graph. It also gives two examples - sketching y = 2x - 1 and y = (x^2 - 1)^(1/2) - and directs the reader to an exercise involving sketching another absolute value function graph.
Ch17 25
This document discusses calculating the limit of the composition of two functions f and g as x approaches a value. For part (a), as x approaches 0 from the positive side, g(x) approaches 2 from the positive side and f(x) approaches negative infinity as x approaches 2 from the positive side. For part (b), as x approaches 5 from the negative side, g(x) approaches positive infinity and as x approaches positive infinity, f(x) approaches 2.
Algebra 1 common factor
The document provides an algebra lesson on factorizing expressions using common factors. It includes examples of expanding and factorizing expressions such as 2(x + 6), ax - bx, and 3x + 18. Students are instructed to complete a factorisation worksheet from an online source to practice these skills. The summary is in 3 sentences.
31. solving quadratic cas_touchpad
This document provides instructions for solving a quadratic equation both algebraically and graphically using a TI-Nspire calculator. It outlines the keystrokes to use the SOLVE() function to solve the equation algebraically and describes how to graph the equation and find the x-intercepts/roots by pressing left/right arrow buttons continuously. The document suggests toggling between the algebraic and graphical windows using up/down arrow buttons to compare the solutions.
DQ
This document contains 5 questions about evaluating various functions:
1) Find f(-8) and f(1) for the function f(x) = x + 8 + 2.
2) Find f(1) and f(-5) for the piecewise function f(x) = x^2 + 2 if x ≤ 1 and f(x) = 2x + 2 if x > 1.
3) Find all values of x such that f(x) = 0 for the function f(x) = 5x + 1.
4) Find the domain of the function h(t) = 4/t.
5) Find the value(s) of x for which
Day 2 Graphing Linear Equations
This document provides instructions for graphing linear equations. It begins with anticipatory questions about solving linear equations. Students are asked to graph the solutions and compare the equations. The document then defines linear equations and explains they graph as straight lines. Examples are given of graphing various linear equations by plotting the solution sets and drawing the line through the points. In the end, students are asked to summarize how the graphed linear equations were similar and different.
Álgebra básica 2
The document contains a 15 question multiple choice algebra test with the following topics covered: solving systems of equations, simplifying algebraic expressions, properties of exponents, rational and irrational numbers, and evaluating expressions. The questions range in difficulty from basic operations to more complex problems involving multiple steps. An answer key is provided at the end listing the correct choice for each question.
8th prealg -l27--oct15
The document discusses laws of exponents and provides examples of applying those laws. Specifically, it introduces the laws that na x nb = na+b, na / nb = na-b, and (na)b = na x b. It also notes that anything to the zero power is equal to one. The examples show applying these laws to simplify expressions and write them as powers of 10, such as 106 x 103 = 109 and 106 / 102 = 104.
ITA 2020 - aberta
The document contains 10 questions regarding mathematics. Question 1 asks to rewrite a function in a specific form, find its minimum value, and determine the point(s) where it assumes the minimum value. Question 2 asks for the probability of each face of 3 dice summing to 9 showing an odd number. Question 3 asks for the radius of a sphere inscribed in a pyramid. The remaining questions involve solving various equations related to geometry, complex numbers, and number theory. The document provides the questions in Portuguese and includes the answers in a separate section.
2 senarai rumus add maths k2 trial spm sbp 2010
The document provides 14 formulae across various topics:
- Algebra formulas for operations, exponents, logarithms
- Calculus formulas for derivatives, integrals, areas under curves
- Statistics formulas for means, standard deviations, probabilities
- Geometry formulas for distances, midpoints, areas of shapes
- Trigonometry formulas for trig functions, angles, triangles
- The symbols used in the formulas are explained.
2 senarai rumus add maths k1 trial spm sbp 2010
The document provides 14 formulae across various topics:
- Algebra formulas for operations, exponents, logarithms
- Calculus formulas for derivatives, integrals, areas under curves
- Statistics formulas for means, standard deviations, probabilities
- Geometry formulas for distances, midpoints, areas of shapes
- Trigonometry formulas for trig functions, angles, triangles
- The symbols used in the formulas are explained.
BBMP1103 - Sept 2011 exam workshop - part 7
This document summarizes an exam preparation workshop on the application of partial differentiation presented by Dr. Richard Ng. It provides the answers to two sample exam questions, finding the critical points and determining whether they are maxima or minima for multivariate functions. For the first question, the critical point is found to be (7/3, 8/3) which is a minimum. For the second question, the critical point is (-4, 2) which is also determined to be a minimum using the second derivative test.
BBMP1103 - Sept 2011 exam workshop - Part 2
This document is a summary of key points from a mathematics exam preparation workshop on differentiation:
1) It provides the solutions to sample differentiation problems, finding the first and second derivatives of functions like f(x)=5x^3 and p(x)=5x^3-3x^2+7/x^2.
2) It also gives the solutions to differentiation questions that were part of past mathematics exams, finding derivatives like dy/dx of functions such as y=(x^3)(4x^2-2x).
3) The document aims to help students preparing for exams by providing worked examples of common differentiation questions and techniques for finding derivatives.
sol page 104 #1,2,3.
This document contains a math lab exercise on graphing rational functions with 4 questions. Question 1 has students predict holes in graphs of rational functions. Question 2 has students predict vertical asymptotes. Question 3 has students predict which graphs have horizontal asymptotes. The document provides step-by-step solutions and explanations for each question.
數學測試
The document discusses mathematical formulas and proofs. It contains:
1) Formulas for polynomials and series expansions using binomial coefficients.
2) A claim and proof about the series expansion of (1-x)-3 using binomial theorem.
3) Notations showing equivalence and equality of expressions.
Pda
Este documento resume las características y funcionalidades de los PDA (ordenadores de bolsillo). Explica que los PDA originalmente se diseñaron como agendas electrónicas con calendarios, listas de contactos y notas, y que actualmente incluyen pantallas táctiles, memoria y conectividad inalámbrica. También destaca algunas ventajas de los PDA como su portabilidad y amplia gama de posibilidades, aunque señala que su precio aún puede ser una limitación para algunos.
Clase1 el conocimiento cientifico
El documento trata sobre los diferentes tipos de conocimiento. Explica que el conocimiento puede ser adquirido de varias maneras, como el conocimiento cotidiano, el conocimiento revelado o religioso, el conocimiento filosófico y el conocimiento científico. Destaca que cada tipo de conocimiento cumple una función distinta y nos permite entender el mundo de diferentes formas, aunque el conocimiento científico se basa en métodos sistemáticos de investigación y está abierto a ser revisado y corregido.
More Related Content
What's hot
Truth, deduction, computation lecture f
This document contains a lecture on functions, λ-calculus, and Peano arithmetic. It defines functions, injections, surjections, bijections, function composition, and identity functions. It introduces λ-calculus, including β-reduction and shows how Church numerals can represent numbers. It then covers Peano arithmetic, defining numbers, addition, multiplication, and exponentiation recursively using λ-terms.
8th Alg - L8.4--March26
This document contains an assignment and lesson on factoring polynomials and solving equations. [1] The assignment is to complete odd problems 2-28 from page 496 in the textbook and Checkpoints 8.1-8.3 by Wednesday. [2] The lesson explains how to factor trinomials that do not have a leading coefficient of 1 by finding two integers whose sum is the coefficient of the x-term and whose product is the constant term. [3] It provides examples of factoring various polynomials and solving equations, checking solutions.
Chapter 16
This document contains a chapter on topics in vector calculus, including exercises on vector fields, divergence, curl, and applications of vector calculus identities and theorems. The exercises involve calculating divergence and curl of various vector fields, applying vector calculus operations like divergence and curl to scalar and vector functions, and manipulating vector calculus identities.
Simultaneous eqn2
1) Simultaneous equations involve two variables in two equations that are solved simultaneously to find the values of the variables.
2) To solve simultaneous equations, one first expresses one variable in terms of the other by changing the subject of one linear equation, then substitutes this into the other equation to obtain a quadratic equation.
3) This quadratic equation is then solved using factorisation or the quadratic formula to find the values of the variables that satisfy both original equations.
Lesson5 Oct14
This document provides steps for sketching the graphs of absolute value functions: sketch the underlying function first, then reflect any parts below the x-axis over the x-axis to obtain the absolute value graph. It also gives two examples - sketching y = 2x - 1 and y = (x^2 - 1)^(1/2) - and directs the reader to an exercise involving sketching another absolute value function graph.
Ch17 25
This document discusses calculating the limit of the composition of two functions f and g as x approaches a value. For part (a), as x approaches 0 from the positive side, g(x) approaches 2 from the positive side and f(x) approaches negative infinity as x approaches 2 from the positive side. For part (b), as x approaches 5 from the negative side, g(x) approaches positive infinity and as x approaches positive infinity, f(x) approaches 2.
Algebra 1 common factor
The document provides an algebra lesson on factorizing expressions using common factors. It includes examples of expanding and factorizing expressions such as 2(x + 6), ax - bx, and 3x + 18. Students are instructed to complete a factorisation worksheet from an online source to practice these skills. The summary is in 3 sentences.
31. solving quadratic cas_touchpad
This document provides instructions for solving a quadratic equation both algebraically and graphically using a TI-Nspire calculator. It outlines the keystrokes to use the SOLVE() function to solve the equation algebraically and describes how to graph the equation and find the x-intercepts/roots by pressing left/right arrow buttons continuously. The document suggests toggling between the algebraic and graphical windows using up/down arrow buttons to compare the solutions.
DQ
This document contains 5 questions about evaluating various functions:
1) Find f(-8) and f(1) for the function f(x) = x + 8 + 2.
2) Find f(1) and f(-5) for the piecewise function f(x) = x^2 + 2 if x ≤ 1 and f(x) = 2x + 2 if x > 1.
3) Find all values of x such that f(x) = 0 for the function f(x) = 5x + 1.
4) Find the domain of the function h(t) = 4/t.
5) Find the value(s) of x for which
Day 2 Graphing Linear Equations
This document provides instructions for graphing linear equations. It begins with anticipatory questions about solving linear equations. Students are asked to graph the solutions and compare the equations. The document then defines linear equations and explains they graph as straight lines. Examples are given of graphing various linear equations by plotting the solution sets and drawing the line through the points. In the end, students are asked to summarize how the graphed linear equations were similar and different.
Álgebra básica 2
The document contains a 15 question multiple choice algebra test with the following topics covered: solving systems of equations, simplifying algebraic expressions, properties of exponents, rational and irrational numbers, and evaluating expressions. The questions range in difficulty from basic operations to more complex problems involving multiple steps. An answer key is provided at the end listing the correct choice for each question.
8th prealg -l27--oct15
The document discusses laws of exponents and provides examples of applying those laws. Specifically, it introduces the laws that na x nb = na+b, na / nb = na-b, and (na)b = na x b. It also notes that anything to the zero power is equal to one. The examples show applying these laws to simplify expressions and write them as powers of 10, such as 106 x 103 = 109 and 106 / 102 = 104.
ITA 2020 - aberta
The document contains 10 questions regarding mathematics. Question 1 asks to rewrite a function in a specific form, find its minimum value, and determine the point(s) where it assumes the minimum value. Question 2 asks for the probability of each face of 3 dice summing to 9 showing an odd number. Question 3 asks for the radius of a sphere inscribed in a pyramid. The remaining questions involve solving various equations related to geometry, complex numbers, and number theory. The document provides the questions in Portuguese and includes the answers in a separate section.
2 senarai rumus add maths k2 trial spm sbp 2010
The document provides 14 formulae across various topics:
- Algebra formulas for operations, exponents, logarithms
- Calculus formulas for derivatives, integrals, areas under curves
- Statistics formulas for means, standard deviations, probabilities
- Geometry formulas for distances, midpoints, areas of shapes
- Trigonometry formulas for trig functions, angles, triangles
- The symbols used in the formulas are explained.
2 senarai rumus add maths k1 trial spm sbp 2010
The document provides 14 formulae across various topics:
- Algebra formulas for operations, exponents, logarithms
- Calculus formulas for derivatives, integrals, areas under curves
- Statistics formulas for means, standard deviations, probabilities
- Geometry formulas for distances, midpoints, areas of shapes
- Trigonometry formulas for trig functions, angles, triangles
- The symbols used in the formulas are explained.
BBMP1103 - Sept 2011 exam workshop - part 7
This document summarizes an exam preparation workshop on the application of partial differentiation presented by Dr. Richard Ng. It provides the answers to two sample exam questions, finding the critical points and determining whether they are maxima or minima for multivariate functions. For the first question, the critical point is found to be (7/3, 8/3) which is a minimum. For the second question, the critical point is (-4, 2) which is also determined to be a minimum using the second derivative test.
BBMP1103 - Sept 2011 exam workshop - Part 2
This document is a summary of key points from a mathematics exam preparation workshop on differentiation:
1) It provides the solutions to sample differentiation problems, finding the first and second derivatives of functions like f(x)=5x^3 and p(x)=5x^3-3x^2+7/x^2.
2) It also gives the solutions to differentiation questions that were part of past mathematics exams, finding derivatives like dy/dx of functions such as y=(x^3)(4x^2-2x).
3) The document aims to help students preparing for exams by providing worked examples of common differentiation questions and techniques for finding derivatives.
sol page 104 #1,2,3.
This document contains a math lab exercise on graphing rational functions with 4 questions. Question 1 has students predict holes in graphs of rational functions. Question 2 has students predict vertical asymptotes. Question 3 has students predict which graphs have horizontal asymptotes. The document provides step-by-step solutions and explanations for each question.
數學測試
The document discusses mathematical formulas and proofs. It contains:
1) Formulas for polynomials and series expansions using binomial coefficients.
2) A claim and proof about the series expansion of (1-x)-3 using binomial theorem.
3) Notations showing equivalence and equality of expressions.
What's hot (20)
Viewers also liked
Pda
Este documento resume las características y funcionalidades de los PDA (ordenadores de bolsillo). Explica que los PDA originalmente se diseñaron como agendas electrónicas con calendarios, listas de contactos y notas, y que actualmente incluyen pantallas táctiles, memoria y conectividad inalámbrica. También destaca algunas ventajas de los PDA como su portabilidad y amplia gama de posibilidades, aunque señala que su precio aún puede ser una limitación para algunos.
Clase1 el conocimiento cientifico
El documento trata sobre los diferentes tipos de conocimiento. Explica que el conocimiento puede ser adquirido de varias maneras, como el conocimiento cotidiano, el conocimiento revelado o religioso, el conocimiento filosófico y el conocimiento científico. Destaca que cada tipo de conocimiento cumple una función distinta y nos permite entender el mundo de diferentes formas, aunque el conocimiento científico se basa en métodos sistemáticos de investigación y está abierto a ser revisado y corregido.
Presentación herraientas colaborativas
Las herramientas colaborativas son sistemas que permiten a los usuarios comunicarse y trabajar juntos sin importar su ubicación física. Algunas de estas herramientas incluyen wikis para editar contenido de forma colaborativa, blogs para compartir información sobre temas específicos, marcadores sociales para compartir enlaces de interés y redes sociales para conectar a comunidades de usuarios en línea. Estas herramientas ofrecen ventajas como la comunicación abierta y participativa que permite generar conocimiento colect
Proyecto de aula
El documento lista 4 integrantes que estudian en la Universidad del Buen Vivir en el curso de nivelación "B" el 24 de junio de 2013.
Plataforma virtual
Este documento define una plataforma virtual como tecnología utilizada para crear cursos en línea que mejoran la comunicación y el aprendizaje a través de la Web 2.0. Explica que Moodle es un software diseñado para ayudar a los educadores a crear cursos en línea de alta calidad y entornos virtuales de aprendizaje. Además, proporciona instrucciones para ingresar a la Plataforma Virtual Moodle escribiendo una dirección URL, seleccionando un curso, buscando el nombre de un profesor y
Producto 6
Este documento describe la importancia de las entrevistas como fuente para estudiar el pasado, proporcionando datos, descripciones y opiniones sobre eventos presenciados. También detalla el huracán Karl en Veracruz en 2010, el cual causó inundaciones e interrupciones eléctricas. El documento proporciona ejemplos de preguntas para una entrevista sobre la experiencia vivida durante el huracán.
Smart messaging
Este documento presenta varios planes de mensajería inteligente total de Claro. Incluye tres planes con diferentes cantidades de minutos, mensajes y datos móviles, así como las condiciones de venta de chips sueltos o equipos desbloqueados con los planes. También proporciona instrucciones para pedir uno de los planes a través de un correo electrónico.
mapa metal
Jean Carlo es un músico que disfruta del rap y el reggaetón. Proviene de una familia compuesta por sus padres y una hermana, y en su tiempo libre le gusta dormir, escuchar música y jugar al fútbol, siendo su equipo favorito la selección nacional.
Sand sculptures burgas 2012
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise stimulates the production of endorphins in the brain which elevate mood and reduce stress levels.
Conselho das finanças públicas
1) O Conselho de Ministros nomeou cinco novos membros para o Conselho Superior das Finanças Públicas, incluindo Maria Teodora Osório Pereira Cardoso como presidente e Jürgen von Hagen como vice-presidente.
2) Rui Nuno Garcia de Pina Neves Baleiras foi nomeado como membro executivo do Conselho, enquanto George Kopits e Carlos José Fonseca Marinheiro foram nomeados como membros não executivos.
3) O Conselho das Finanças Públicas é um órgão independente criado para pronunciar-se sobre objetivos macroe
Evaluación del desempeño
La evaluación del desempeño es un proceso formal para determinar cómo los empleados están realizando su trabajo en relación con los estándares establecidos. Esto ayuda a identificar a los buenos empleados y su potencial para otros puestos. La responsabilidad de la evaluación depende de la política de recursos humanos de la organización, que puede ser centralizada, descentralizada o una combinación de ambas. Existen varios métodos para realizar evaluaciones, como escalas, registros observacionales y métodos centrados en eventos críticos. Factores como criterios
Q2
The magazine primarily attracts young people aged 16-25 due to its rebellious style featuring a rock star model. While the magazine portrays stereotypical rock star imagery like tattoos and dark makeup, the in-depth interview features reveals the model does not support harmful stereotypes. The interview discusses the model's philanthropic animal foundation and family life outside London to provide perspective beyond superficial appearances. Although mostly featuring white heterosexual males, the magazine aims to be open-minded and available to all groups.
Expocicon catedra
Este documento resume diferentes procesos académicos como homologación, validación y cambio de jornada que permiten la movilidad estudiantil en situaciones especiales. También describe los procesos de evaluación con dos notas parciales y nota final, así como distinciones y estímulos para estudiantes con alto desempeño.
Viewers also liked (19)
Similar to Graphing and Solving for Zeros
5.1 vertex symm t-table
This document provides instructions for graphing quadratic functions by finding the vertex and axis of symmetry. It gives examples of graphing functions like f(x)=3x^2-6x+1 and finding that the vertex is the maximum or minimum point. It also covers graphing using transformations, with examples of shifting and stretching quadratic functions and finding corresponding vertices and axes of symmetry.
8th alg -l3.4--nov5
This document discusses direct variation and proportional relationships. It defines direct variation as an equation in the form y=kx, where k is the constant of variation or constant of proportionality. Direct variation equations are always linear relationships that pass through the origin. Some examples of direct variation equations are graphed and their constants of variation and slopes are identified. The document also provides examples of writing direct variation equations and solving for unknown variables when some variables are given.
Exercise #11 notes
This document discusses graphing absolute value functions. It provides examples of graphing various absolute value functions, including f(x)=|x|^2, f(x)=2|x|-1, f(x)=|x|^2-1, f(x)=3|x|^2-4, f(x)=|cos(x)|, f(x)=2|x|-3-1, and shows how to write a piecewise function definition for f(x)=|x|^2. The graphs are V-shaped and symmetric about the y-axis, with vertices at the points where the absolute value terms are equal to zero.
8th alg -l3.2--nov1
1) The document provides instructions for a math lesson assignment on linear functions and solving equations. Students are to complete practice problems from their textbook and sign up for extra credit on an earlier test.
2) The warmup exercises involve solving various equations algebraically. The lesson defines linear functions and their relationship to roots/zeros, discussing how to graphically and algebraically solve linear equations by setting them equal to zero.
3) Examples are shown of solving equations both graphically by sketching the line and algebraically by isolating the variable, such as solving 0 = 1/2x - 2 for x = 4.
Double integration
This document provides examples and explanations of double integrals. It defines a double integral as integrating a function f(x,y) over a region R in the xy-plane. It then gives three key points:
1) To evaluate a double integral, integrate the inner integral first treating the other variable as a constant, then integrate the outer integral.
2) The easiest regions to integrate over are rectangles, as the limits of integration will all be constants.
3) For non-rectangular regions, the limits of integration may be variable, requiring more careful analysis to determine the limits for each integral.
Lesson 6 Nov 23 24 09
The document provides examples of using implicit differentiation to find derivatives. It demonstrates:
1) Taking the derivative of each side of an equation and putting all terms with dy/dx on one side.
2) Factoring out dy/dx from the resulting equation.
3) Solving for dy/dx.
Several examples are worked through, including finding the derivative of equations, finding the slope of a tangent line at a point, and using the product rule. The document concludes with an exercise involving implicit differentiation.
2.2 Polynomial Function Notes
The document discusses polynomial functions, including how to graph common polynomials, find zeros of polynomials, and write polynomials given their roots. It provides examples of matching polynomial equations to their graphs, finding the real zeros of polynomials by factoring, and writing polynomials when given the roots. The document also covers how to use a graphing calculator to find the zeros of polynomials.
Remedial mtk
1. The student's name is Azizaty Desiana. She is in class XI IPS 1. Her average score is 41.5. The test had 20 questions.
2. The document provides examples of math problems and questions about functions. It asks for the limit of various expressions as variables approach certain values.
3. The questions are assessing knowledge of functions, inverses, limits, and calculations involving algebraic expressions.
Lesson 24
The document contains problems involving evaluating trigonometric functions, combining trigonometric functions, and combining other functions. Problem 1 asks to evaluate the sum of cosine of 60 degrees and sine of 45 degrees. Problem 2 asks to evaluate the sum of tangent of 30 degrees and cosine of 45 degrees. Problem 3 asks to evaluate the sum of tangent of 45 degrees and twice tangent of 30 degrees.
Jejemon
This document is a take-home exam for a mathematics course. It contains 3 sections with multiple questions each: 1) limits of multivariable functions, 2) partial differentiation, and 3) tangent planes and differentials. Students are instructed to show their work and solutions independently in a blue book and submit it by a specified deadline.
Inverse of functions
The document defines one-to-one functions and their inverses. A one-to-one function maps each element in the domain to a unique element in the range. The inverse of a one-to-one function undoes the original mapping. To find the inverse function algebraically, interchange the x and y variables and isolate y. Graphically, flip the graph across the line y=x to find the inverse. Examples are provided of finding inverses both algebraically and graphically. Homework problems involve finding specific inverses and their domains and ranges.
Exercise #10 notes
This document provides examples for graphing reciprocals of functions. It explains that for reciprocals, smaller numbers on the x-axis become larger on the y-axis, and vice versa. An example graphs the reciprocal of f(x)=1/x^2. It notes that reciprocals can be written in the form f(x)=k/x+h, where k and h are determined from the original function. Further examples graph the reciprocals of f(x)=2/x+4 and f(x)=sin(x).
Integral (area)
The document discusses using definite integrals to find the area under a curve. It provides examples of finding the area of various shaded regions bounded by curves and the x-axis using the formula: area = ∫f(x)dx from x=a to x=b. It also shows how to find the coordinates of points where two curves intersect in order to divide the region into multiple areas and calculate them separately.
Pc12 sol c04_cp
This document contains sample solutions to checkpoint questions about combining functions. It provides the steps to:
1) Sketch the graph of y = f(x)/g(x) given the graphs of y = f(x) and y = g(x)
2) Write explicit equations for functions like g(x), h(x), and k(x) that satisfy an equation like f(x) = g(x) - h(x) - k(x)
3) Determine the domain and range of functions formed by combining basic functions using operations like addition, subtraction, multiplication, and division.
Pc12 sol c04_cp
This document contains sample solutions to checkpoint questions about combining functions. It provides the steps to:
1) Sketch the graph of y = f(x)/g(x) given the graphs of y = f(x) and y = g(x)
2) Write explicit equations for functions like g(x), h(x), and k(x) that satisfy an equation like f(x) = g(x) - h(x) - k(x)
3) Determine the domain and range of functions formed by combining basic functions using operations like addition, subtraction, multiplication, and division.
Chapter 3
1) A quadratic function is an equation of the form f(x) = ax^2 + bx + c, where a ≠ 0. Its graph is a parabola.
2) The vertex of a parabola is the point where it intersects its axis of symmetry. If a > 0, the parabola opens upward and the vertex is a minimum. If a < 0, it opens downward and the vertex is a maximum.
3) The standard form of a quadratic equation is f(x) = a(x - h)^2 + k, where the vertex is (h, k) and the axis of symmetry is x = h.
Exponential functions
The document discusses exponential functions of the form f(x) = ax, where a is the base. It defines exponential functions and provides examples of evaluating them. The key aspects of exponential graphs are that they increase rapidly as x increases and have a horizontal asymptote of y = 0 if a > 1 or y = 0 if 0 < a < 1. Examples are given of sketching graphs of exponential functions and stating their domains and ranges. The graph of the natural exponential function f(x) = ex is also discussed.
125 5.4
The document defines a definite integral as the integral of a function over a bounded interval from a to b, written as ∫f(x)dx from a to b. This represents the area under the curve of the function f(x) between the bounds a and b. Several examples are provided of calculating definite integrals to find the area under curves over given intervals using the Fundamental Theorem of Calculus. It is noted that definite integrals cannot result in negative area values.
Business math
This document provides an introduction to basic definite integration. It defines definite integration as calculating the area under a curve between two limits using antiderivatives. It demonstrates how to calculate definite integrals of simple functions and interpret the results as areas. It also discusses how the sign of the integral depends on whether the function lies above or below the x-axis. Quizzes are included to assess understanding of these concepts.
Zeros of p(x)
This document discusses various methods for finding the zeros or roots of polynomial functions, including factoring, factor theorem, synthetic division, and using the principle that every polynomial of degree n has n zeros. It provides examples of finding the zeros of polynomials by factorization, using a given zero to find other zeros through synthetic division, and identifying which numbers are zeros of various polynomials. Exercises are included for students to practice finding remaining zeros given one zero and identifying polynomial factors.
Similar to Graphing and Solving for Zeros (20)
More from andreagoings
To know test 17
This document contains a list of mathematical and statistical concepts to study for an upcoming test, including graphing systems of inequalities, standard deviation, properties of parabolas, trigonometric functions, linear variation, elimination methods for solving systems of equations, properties of logarithmic graphs, the relationship between voltage, resistance and current, calculating variance and standard deviation with and without a calculator, finding the area of triangles, average rate of change, properties of antilogarithms, polar and rectangular coordinate systems, and properties of circles.
Lesson 72
This document discusses using the Law of Sines to solve triangles when one side and two other parts are known. It provides three example triangles, labeling one side and two angles for each, and asks the reader to solve for the unknown parts. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is equal to the ratios for the other two sides. This allows one to determine missing side lengths or angles when one side and two other parts are known.
Lesson 71
An ellipse is defined as the set of all points such that the sum of the distances from the point to two fixed foci points is a constant. The major axis is the longest side of the ellipse, and the two fixed points are called the foci. The standard form of the ellipse equation is (x/a)^2 + (y/b)^2 = 1, where a is half the length of the major axis and b is half the length of the minor axis.
Lesson 70
The document discusses using percentiles and z-scores to compare test scores from one year to the next. It provides information on calculating z-scores as a way to determine percentiles and compare a student's score to the mean and standard deviation from the previous year. It then asks three questions about determining percentiles based on the mean and standard deviation of baby weights at a hospital over seven years.
Lesson 69
The document defines a matrix as a rectangular array of numbers, with elements being the individual numbers. For matrices to be equal, they must be the same size and have matching corresponding elements. A square matrix is one where the number of rows equals the number of columns. Any square matrix will have a determinant value that can be calculated. The document then provides examples of evaluating the determinants of different sized matrices and solving for unknown values within matrices.
To Know Test 16
This document contains a list of mathematical concepts and problems including finding the area of geometric shapes like trapezoids, using formulas like the volume formula, plotting data, graphing functions like sinusoidal functions, working with complex numbers, logarithms, rates of change, systems of inequalities, statistics like mean, variance and standard deviation, derivatives, completing the square, areas of segments of circles, and evaluating and graphing trigonometric functions.
Lesson 68
This document defines and discusses parabolas using the locus definition. It states that a parabola is the locus of all points that are equidistant from a fixed point (the focus) and a fixed line (the directrix). The document provides examples of finding the equation of a parabola given the focus and directrix, as well as shifting the vertex. It also discusses applications of parabolic reflectors and how to place a receiver at the focus of a rotating parabolic antenna based on the given equation.
12.1 day 2
The first triangle has angles of 60 and 30 degrees with opposite sides of 4 and x, finding x to be 8 using trigonometric functions. The second triangle has angles of 25 and 63 degrees with opposite sides of 10 and x, finding x to be 6 using trigonometric functions. The third problem asks how far (x) a plane is from its landing spot, given the angle is 15 degrees and the opposite side is 800 feet, finding x to be 800/tan(15) = 1200 feet using trigonometric functions.
12.1 sin cos tan
This document discusses trigonometric functions like sine, cosine, and tangent. It defines the trig functions using ratios of sides of a right triangle. It then provides examples of evaluating the six trig functions for various angles in different right triangles, as well as examples of using trig functions to solve for unknown side lengths of right triangles.
Lesson 67
The document discusses antilogarithms and how they are the inverse operation of logarithms. It states that the antilogarithm of a number is equal to the exponent when that number is the logarithm of the base. It then provides examples of finding the antilogarithm of 4.63 for different bases, including bases 2, 10, and the mathematical constant e, which is approximately equal to 2.71828.
Lesson 66
This document discusses formulas for solving systems of equations, calculating phase shifts in sinusoidal functions, and accounting for changes in period. It provides the general formulas for solving a system of two equations with two unknowns. It also explains that if the period of a sinusoid is not 2π or 360°, the coefficient must be calculated by dividing 360° or 2π by the actual period. Finally, it notes that if given a sinusoid with an amplitude, center, coefficient, phase angle, and period, both the sine and cosine equations can be written.
Lesson 65
This document provides 3 problems involving radicals in trigonometric equations, graphs of logarithms. The first two problems ask the reader to solve trigonometric equations containing radicals given certain conditions. The third problem asks the reader to sketch the graph of the logarithmic function y = log3.5 x.
11.6 geometric sequences
This document discusses geometric sequences and provides examples of calculating terms of geometric sequences given initial terms and common ratios. It also covers finding geometric means between two terms by taking the square root of the product of the terms. Examples include finding the 6th term of the sequence 3, -12, 48, -192, finding the 7th term of a sequence where the 2nd term is 24 and 5th term is 3, and finding geometric means between 4 and 9 by taking the square root of their product.
To know test 15
This document contains a list of mathematical concepts and problems including equations of circles, logarithms, trigonometric functions, permutations, systems of inequalities, areas, factoring complex numbers, and properties of circles, lines, and graphs. It appears to be a study guide or checklist for reviewing multiple topics in precalculus or calculus.
Lesson 63
This document contains 3 problems involving completing the square to write equations of circles in standard form and graphing the circles. Problem 1 has the equation x^2 + y^2 - 6x + 8y + 21 = 0 and asks to complete the square and graph the circle. Problem 2 gives the equation x^2 + y^2 + 4x - 6y + 6 = 0 and asks to do the same. Problem 3 gives the equation 2x^2 + 2y^2 - x + y - 3 = 0 and asks to complete the square and describe the resulting circle.
11.5 arithmetic sequences
The document discusses arithmetic sequences and how to find specific terms (tn) using the common difference (d) between terms. It explains that the general formula for an arithmetic sequence is tn = a1 + (n-1)d, where a1 is the first term and d is the common difference. It then provides examples of using this formula to find the nth term for given arithmetic sequences and finds the arithmetic mean between two numbers.
11.3 sequences
The document contains instructions for finding terms of different sequences. It defines a sequence where the first term is 4 and each subsequent term is half of the previous term. It also defines a Fibonacci sequence where the first two terms are 1 and each term is the sum of the previous two terms. It asks the reader to find the first five terms of these sequences.
Lesson 62
This document discusses solving linear equations for variables x and y. It also presents a real world example where the total cost of producing a product varied linearly with the number produced. When 100 were produced the cost was $700, and when 400 were produced the cost was $2200. An equation is given to model this linear relationship between cost (C) and number produced (N) as C = mN + b.
Lesson 61
This document discusses analyzing data through measures like the mean, standard deviation, and box and whisker plots. It provides examples of calculating the mean and standard deviation for different data sets. It also discusses how the standard deviation indicates how data points are distributed around the mean. Finally, it includes an example of using a graphing calculator to analyze a data set and draw a box and whisker plot.
11.2 multiplying matrices
The document discusses matrix multiplication. It explains that two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix. It provides an example of multiplying two matrices by multiplying the elements in each row of the first matrix with each column of the second matrix and adding the products. It then provides examples of multiplying specific matrices and determining if the products are defined based on the dimensions of the matrices.
More from andreagoings (20)
Recently uploaded
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdMain Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcBBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingExcellence Foundation for South Sudan
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
ANATOMY AND BIOMECHANICS OF HIP JOINT.pdf
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
DRUGS AND ITS classification slide share
Any substance (other than food) that is used to prevent, diagnose, treat, or relieve symptoms of a
disease or abnormal condition
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Recently uploaded (20)
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Graphing and Solving for Zeros
- 1. graphing and solving for zeros.notebook October 17, 2012 Recall: y = x + 3 yintercept= xintercept= 1
- 2. graphing and solving for zeros.notebook October 17, 2012 f(x) = x2 x y 2 1 0 1 2 2
- 3. graphing and solving for zeros.notebook October 17, 2012 f(x) = x2 4x + 3 yintercept= find the zeros (when y = 0) x y 0 1 2 3 4 3
- 4. graphing and solving for zeros.notebook October 17, 2012 f(x) = x2 + 4x +5 yintercept= find the zeros x y 0 1 2 3 4 4