Quadratic function and its graph using geogebra
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This document discusses quadratic functions and how to graph them using Geogebra. A quadratic function is defined as a function of the form f(x) = ax^2 + bx + c, where a, b, and c are integers. The graph of a quadratic function is a parabola. Examples are given of graphing the quadratic functions f(x) = x^2, f(x) = 1/2x^2, and f(x) = 2x^2 - 4x - 6. Formulas are provided for calculating the vertex coordinates of a parabola based on the values of a, b, and D, where D is the discriminant. The shape of the parab
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Class XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solutionPratima Nayak ,Kendriya Vidyalaya Sangathan
The document is a sample question paper for Class XII Mathematics. It consists of 3 sections - Section A has 10 one-mark questions, Section B has 12 four-mark questions, and Section C has 7 six-mark questions. All questions are compulsory. The paper tests concepts related to matrices, trigonometry, calculus, differential equations, and vectors. Internal choices are provided in some questions. Calculators are not permitted.Quadratic Functions (a) table of values (b) graph (c)equation.pptx
This document discusses three ways to analyze and represent quadratic functions: using a table of values, graphically, and using the equation. It provides an example of each: (1) a table of values is generated for f(x) = 2x^2 - 3x + 1 with x-values from -2 to 2, (2) the graph of this function is a parabola that opens upward based on the positive coefficient, (3) the equation provides information like the vertex at (3/4, 1/8) and axis of symmetry at x = 3/4. Representing the function using all three methods provides a comprehensive understanding.
Quadratic Functions (a) table of values (b) graph (c)equation.pptx
This document discusses three ways to analyze quadratic functions: using a table of values, graphically, and using the equation. It provides an example of each: (1) a table of values is generated for f(x)=2x^2-3x+1 with x values from -2 to 2, (2) the graph of this function is a parabola that opens upward based on the positive coefficient, (3) the equation provides information like the vertex at (3/4, 1/8) found using the quadratic formula. Representing functions in these different ways provides a comprehensive understanding.
Pptpersamaankuadrat 150205080445-conversion-gate02
This document discusses quadratic equations and functions. It explains how to solve quadratic equations by factoring, completing the square, and using the quadratic formula. It also discusses using the discriminant to determine the number and type of roots. Properties of quadratic functions such as the sum and product of roots are covered. Methods for constructing quadratic equations and functions given certain properties are provided. Finally, it briefly discusses sketching the graph of a quadratic function.
Module 2 quadratic functions
1. This module covers quadratic functions and how to graph them. Students will learn to identify the vertex, axis of symmetry, and direction of opening of quadratic graphs.
2. Key aspects covered include how changing coefficients a, h, and k affect the width, translation, and vertical shift of the graph. When a increases, the graph narrows; changing h translates the graph left or right; and changing k shifts the graph up or down.
3. The steps for graphing a quadratic function are finding the vertex, axis of symmetry, direction of opening, and making a table of values to plot points.
Algebra 1
The document discusses transformations of linear functions. It provides examples of translating graphs vertically and horizontally by adding or subtracting values from inputs and outputs. It also discusses reflecting graphs over the x-axis or y-axis by multiplying inputs or outputs by -1. Horizontal and vertical stretches and shrinks are described as multiplying the inputs or outputs by a scale factor. The key is that transformations preserve the shape of the graph but can change its position, orientation, or scale.
Quadratics Final
The document discusses three forms of quadratic equations - standard, vertex, and intercept form - and how to graph each. It provides the key characteristics and steps to graph quadratics in each form. It also discusses two special factoring patterns for standard form and how to convert between the three forms.
Algebra formulas
This document provides an algebra cheat sheet that summarizes many common algebraic properties, formulas, and concepts. It covers topics such as arithmetic operations, properties of inequalities and absolute value, exponent properties, factoring formulas, solving equations, graphing functions, and common algebraic errors. The cheat sheet is a concise 3-page reference for the basics of algebra.
Mathematics 9 Quadratic Functions (Module 2)
This learner's module will discuss or talk about the Graph of Quadratic Functions. It will also discuss on how to draw the Graph of Quadratic Functions using the vertex, axis of symmetry, etc.
Quadratic
The document discusses quadratic functions. It defines quadratic functions as functions of the form f(x) = ax^2 + bx + c where a ≠ 0. It explains that the graph of a quadratic function is a parabola. If a>0, the parabola opens up and there is a minimum point. If a<0, the parabola opens down and there is a maximum point. The roots of the quadratic function correspond to the x-intercepts of the graph. If b^2 - 4ac > 0 there are two distinct roots, if b^2 - 4ac = 0 there is one repeated root, and if b^2 - 4ac < 0 there are no real roots
02.21.2020 Algebra I Quadraic Functions.ppt
The document provides an agenda and lesson plan for an Algebra I class that includes the following:
1. The class will begin with a D.E.A.R activity called "Jaguar Ascensions" followed by taking Cornell notes on the lesson.
2. Students will then summarize their notes and have a teacher dialogue.
3. A number sense routine involving finding a missing number in an equation will be completed.
4. The remainder of the class will cover topics on quadratic functions including graphing quadratic functions in standard, vertex, and intercept forms as well as solving quadratic equations through factoring and using the quadratic formula.
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Class XII CBSE Mathematics Sample question paper with solution
Class XII CBSE Mathematics Sample question paper with solution
Quadratic Functions (a) table of values (b) graph (c)equation.pptx
Quadratic Functions (a) table of values (b) graph (c)equation.pptx
Quadratic Functions (a) table of values (b) graph (c)equation.pptx
Quadratic Functions (a) table of values (b) graph (c)equation.pptx
Pptpersamaankuadrat 150205080445-conversion-gate02
Pptpersamaankuadrat 150205080445-conversion-gate02
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პროპორცია
მოსწავლეებმა განივითარონ შეფარდებისა და პროპორციის გამოყენების უნარ-ჩვევები ამოცანათა ამოსახსნელად;
მოსწავლეები დაეუფლონ პროპორციული სიდიდეების, პროპორციული დამოკი-დებულებების ცნებასა და სათანადო გეომეტრიულ წარმოდგენას;
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Quadratic function and its graph using geogebra
- 1. QUADRATIC FUNCTION AND ITS GRAPH USING GEOGEBRA
- 2. FUNCTION OF ARE GIVEN BY THE FOLLOWING FORMULA, WHERE THE DEPENDENT VARIABLE X, A,B,C INTEGERS IS CALLED A QUADRATIC FUNCTION. 0;)( 2 ≠++= acbxaxxF The graph of a quadratic function is a parabola
- 3. If a> o branches directed to the top of the parabola, and if a <o - down. Consider the case: a> 0; b = 0 and c = 0 and using Geogebra-build f (x) = 2x ^ 2 and f (x) = 1/2x ^ 2 schedule
- 5. Fill the table and build one daimave The graph of y = x ^ 2 and y = (x-2) ^ 2 schedule x -3 -2 -1 0 1 2 3 Y=x^2 Y=(x- 2)^2
- 7. Build y = 2x ^ 2-4x-6 Quadratic Graphs Parabola vertex coordinates are calculated by the formula: m=-D/4a n=-b/2a
- 8. When D>0 and a>0 Schedule has a face
- 9. When D=0 and a>0 Schedule has a face
- 10. When D<0 and a>0 Schedule has a face
- 11. When D>0 and a<0 Schedule has a face
- 12. When D=0 and a<0 Schedule has a face
- 13. When D<0 and a<0 Schedule has a face