Graphing A Parabola
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The document discusses how to find the axis of symmetry and turning point of a parabola. The axis of symmetry is the line that cuts the parabola into two equal halves and passes through the turning point. The formula to find the axis of symmetry is x=-b/2a. For the parabola y=x^2+6x-2, the axis of symmetry is x=3 and the turning point is (3,25). An example is then given to find the axis of symmetry and turning point of y=x^2-6x+8.
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2) The axis of symmetry always passes through the vertex. The y-intercept can be found by substituting x=0 into the function.
3) A quadratic function has either 0, 1, or 2 solutions which are found by setting the function equal to 0 and solving the resulting quadratic equation.
Quadratic equations (Minimum value, turning point)
How to find the minimum and maximum value of a quadratic equation
How to find the Y-intercept of a quadratic graph and equation
How to calculate the equation of the line of symmetry of a quadratic curve
How to find the turning point (vertex) of a quadratic curve, equation or graph.
chapter1_part2.pdf
1. This document discusses linear equations, slope, graphing lines, writing equations in slope-intercept form, and solving systems of linear equations.
2. Key concepts explained include slope as rise over run, the different forms of writing a linear equation, finding the x- and y-intercepts, and using two points to write the equation of a line in slope-intercept form.
3. Examples are provided to demonstrate how to graph lines based on their equations in different forms, find intercepts, write equations from two points, and solve systems of linear equations.
Quadratic Equations Graphing
The document discusses how to graph quadratic functions of the form y = ax^2 + bx + c. It explains that the graph is a parabola that may open up or down. It describes how to find the line of symmetry, which is -b/2a, and how this line passes through the vertex. It provides steps to find the vertex by plugging the x-value from the line of symmetry into the original equation. Finally, it demonstrates graphing a parabola by finding two additional points and reflecting them across the line of symmetry.
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.
Graphing quadratic equations
1) This document discusses how to solve quadratic equations by graphing, including identifying the terms of a quadratic equation, finding the solutions by graphing, and graphing quadratic functions.
2) The key steps for graphing a quadratic function are to find the axis of symmetry using the standard form equation, find the vertex point, and find two other points to reflect across the axis of symmetry to complete the parabolic graph.
3) An example problem walks through graphing the quadratic equation y = x^2 - 4x by first finding the roots, vertex, and axis of symmetry, and then constructing a table to plot points and graph the parabola.
Graphing Quadratics
This document provides information about graphing quadratic functions. It defines the standard form of a quadratic function as y = ax^2 + bx + c and explains that the sign of a determines if the parabola opens up or down. It describes how to find the axis of symmetry, vertex, domain and range. The steps to graph a quadratic function are given as finding the axis of symmetry, the vertex, and then two other points to reflect across the axis and connect with a smooth curve. Methods for finding the axis of symmetry, vertex, y-intercept and solutions are demonstrated through examples.
G9_Q2_W2_L2_GraphsofQUadraticFunction.pdf
The document discusses key concepts about quadratic functions including:
1) Quadratic functions can be represented by the equation f(x) = ax^2 + bx + c and form a parabolic shape that can open up or down.
2) The axis of symmetry of a parabola passes through the vertex (highest/lowest point) and can be found using the equation x = -b/2a.
3) The vertex coordinates can be determined by substituting the axis of symmetry value into the original equation.
4) Quadratic functions can have 0, 1, or 2 x-intercepts depending on the number of real solutions to the related quadratic equation.
6.6 analyzing graphs of quadratic functions
This document discusses analyzing and graphing quadratic functions. It defines key terms like vertex, axis of symmetry, and vertex form. It explains that the graph of y=ax^2 is a parabola, and how the value of a affects whether the parabola opens up or down. It also describes how to graph quadratic functions in vertex form by plotting the vertex and axis of symmetry, and using symmetry.
6. 1 graphing quadratics
The document discusses graphing quadratic functions. It defines a quadratic function as an equation of the form y=ax^2 +bx+c where a ≠ 0, forming a U-shaped parabola. It explains that the vertex is the highest/lowest point and the axis of symmetry is the vertical line through the vertex. It provides steps for graphing a quadratic function by finding the vertex coordinates using the standard form equation, choosing x-values on each side of the vertex, calculating corresponding y-values, and plotting points connected with a smooth curve. An example problem demonstrates these steps.
Algebra 2. 9.16 Quadratics 2
This document provides examples and explanations for identifying key properties of quadratic functions presented in standard form, including:
1. Determining whether the graph opens upward or downward based on the sign of the leading coefficient a.
2. Finding the axis of symmetry by setting b/2a equal to x.
3. Finding the vertex by substituting the x-value from the axis of symmetry into the original function to determine the y-value.
4. Identifying the y-intercept from the constant term c.
Steps are demonstrated for graphing quadratic functions based on these properties, finding minimum/maximum values, and stating the domain and range. Examples analyze functions algebraically and graphically.
4.2 stem parabolas revisited
The document discusses how to graph quadratic equations in the form of y = ax^2 + bx + c. It states that the graphs are parabolas with a vertex and center line. To graph a parabola, one finds the vertex, another point such as the y-intercept, reflects that point across the center line, and finds the x-intercept to complete the parabola.
Notes 3-4
This document discusses symmetries of graphs and functions. It defines reflection symmetry, axis/line of symmetry, point/center of symmetry, and symmetry with respect to the x-axis or y-axis. It provides examples of proving symmetry of graphs like y=x^2 and y=x. It also defines even and odd functions and discusses using the graph-translation theorem to find asymptotes. The homework assigned is problems 1 through 21 on page 183.
WRITING AND GRAPHING LINEAR EQUATIONS 1.pptx
The document discusses linear equations and graphing linear relationships. It defines key terms like slope, y-intercept, x-intercept, and provides examples of writing linear equations in slope-intercept form and point-slope form given certain information like a point and slope. It also discusses using tables and graphs to plot linear equations and find slopes from graphs or between two points. Real-world examples of linear relationships are provided as well.
identities1.2
The document discusses the concept of slope and how it is used to describe the steepness of a line. It defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. Several forms of linear equations are presented, including point-slope form, slope-intercept form, and standard form. Relationships between parallel and perpendicular lines based on their slopes are also described. Examples are provided to demonstrate finding slopes, writing equations of lines, and determining if lines are parallel or perpendicular based on their slopes.
Graphquadraticfcns2
The document provides information about graphing quadratic functions in standard form (y=ax^2 + bx + c). It discusses that the graph is a parabola that opens up or down depending on whether a is positive or negative. It also explains that the line of symmetry for the parabola is given by x=-b/2a and the vertex is found by plugging the x-value from the line of symmetry into the original equation. Finally, it demonstrates graphing a quadratic function in standard form using three steps: finding the line of symmetry, finding the vertex, and finding/reflecting two other points to connect with a smooth curve.
Graph Quadratics
The document discusses graphing quadratic functions in standard form (y=ax^2 + bx + c). It explains that the graph is a parabola that can open up or down depending on whether a is positive or negative. The line of symmetry for the parabola passes through the vertex and is given by the equation x=-b/2a. The steps to graph are: 1) find the line of symmetry, 2) plug the x-value into the original equation to find the vertex, 3) find two other points and reflect them across the line of symmetry.
Geo 3.6&7 slope
Reveiws slope from algebra I, then shows how to find lines parallel and perpendicular to a given line through a given point.
DIFFERENTIATION
1) The document discusses differentiation and various techniques for taking derivatives of functions with respect to variables like x and y. This includes the derivative of sums, constants, products, quotients, exponentials, logarithms and inverse trigonometric functions.
2) Applications of differentiation like finding rates of change, tangents, normals, and stationary points are covered. Techniques for finding maximum/minimum values using derivatives are presented.
3) Series expansions like Maclaurin and Taylor series are introduced to approximate functions as polynomials. The concept of partial derivatives is defined for functions with two variables.
Coordinategeometry1 1
The document discusses coordinate geometry and defines key terms like axes of reference, coordinates of a point, distance formula, section formula, and area of a triangle. It provides examples of using these concepts and formulas to solve problems like finding the coordinates of a point dividing a line segment in a given ratio, or the area of a triangle given the coordinates of its vertices.
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Graphing A Parabola
- 1. Graphing a parabola GQ: What is the axis of symmetry? What is the turning point?
- 2. Every parabola as an axis of symmetry, a line that cuts the parabola into two equal halves. In this picture, the axis of symmetry is x=0. The axis of symmetry goes through a point called the turning point. The turning point of this parabola is (0,1).
- 3. The formula for the axis of symmetry is x=-b/2a. Find the axis of symmetry of y=x2 + 6x – 2. A = 1 B = 6 C = -2 X = -b/2a = -6/2(1) = -3 So x = 3