Lesson 25

# Lesson 25 - Lesson 25 Quadratic Function a function is...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lesson 25 Quadratic Function: - a function is quadratic if it is in any of the following forms: o () , where ( ) o () , where ( )( ), where o () - the degree of a quadratic function is _______ - the graph of a quadratic function a parabola Vertex of a parabola: - the turning point, the point where the graph of a quadratic function changes from increasing to decreasing, or vice versa - the -coordinate of the vertex is either the maximum or minimum function value - the -coordinate of the vertex is the input where the maximum or minimum function value occurs Example 1: Graph the following quadratic functions. List the vertex and any symmetry. a. ( ) b. ( ) b. ( ) The graph of a quadratic function is a parabola that opens up or down (why can’t it open to the left or right?). If the leading coefficient , the parabola opens up; if the leading coefficient , the parabola opens down (why can’t the leading coefficient ?). The graph of a quadratic function will always be symmetric about a vertical line called the line of symmetry. Example 2: Graph the following functions by transforming the graph of the function ( ) . Find the vertex of each and list any symmetry. ) ( ) a. ( ) ( b. ( ) c. ( ) Can you determine the vertex of each graph without graphing? Can you determine the line of symmetry for each graph without graphing? Standard Equation of a Parabola with Vertical Axis: ( ) ) - the vertex is ( - when , the parabola opens _______ - when , the parabola opens _______ - symmetric about the line , where is the -coordinate of the vertex When a quadratic function, such as () is written in the form of the standard equation of a parabola with a vertical axis ( ) the vertex is ( ), the line of symmetry is sketched by transforming the basic parabola units to the right and 2 units up). , and the graph can be (shift the graph 3 How can a quadratic function of the form ( ) ( ) converted to the form ( ) ? How can ( ) be written in the form be ( ) ? Example 3: Given the following functions, find the standard equation of the parabola, then graph and find the following: a. ( ) () () when b. ( ) () () when c. ( ) () () d. ( ) () () when ( when )( ) Example 4: Find the standard equations of the parabolas shown: a. b. c. d. Looking back at the graphs in previous two examples, do you notice a relationship between the -coordinate of the vertex and the -intercepts? Example 5: Find the standard equation of a parabola with a vertical axis that satisfies the given conditions: ) a. Vertex ( ), passing through ( b. Vertex ( c. -intercepts ), -intercept and , minimum value of ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online