Download presentation

Presentation is loading. Please wait.

Published byMyrtle Norma Davis Modified over 3 years ago

1
FURTHER GRAPHING OF QUADRATIC FUNCTIONS Section 11.6

2
Further Graphing of Quadratic Functions Section 11.6 Graph a quadratic equation by plotting points. Identify the vertex of a parabola.

3
Quadratic Functions and Their Graphs Graph by plotting points. XY -2 0 1 2 Section 11.6 XY -2-3 -4 0-3 10 27

4
Quadratic Functions and Their Graphs Graph by plotting points. Quadratic Function A function that can be written in the form y = ax 2 + bx + c, where a, b, and c are real numbers and a ≠ 0. The shape of the graph of a quadratic function is called a parabola. The maximum or minimum value is called the vertex and has ordered pair (h, k). All parabolas have an axis of symmetry, which is a vertical line running through the vertex, equation x = h. Section 11.6 Vertex (-1, -4) Axis of symmetry x = -1

5
Quadratic Functions and Their Graphs Solve. Quadratic Function A function that can be written in the form y = ax 2 + bx + c, where a, b, and c are real numbers and a ≠ 0. Solving the equation equal to zero is the same as saying y=0, or finding the x- intercepts. Because of symmetry, the x- intercepts will be equidistant from the vertex. Section 11.6 Vertex (-1, -4) Axis of symmetry x = -1

6
Quadratic Functions and Their Graphs Section 11.6 Given an equation of the form y = ax 2 + bx + c, the equation of the axis of symmetry can be found using the formula: Since the axis of symmetry runs through the vertex, this formula also finds the x-coordinate of the vertex. To get the y-coordinate, substitute the found x-coordinate back into the quadratic equation.

7
Deriving a Formula for Finding the Vertex Section 11.6 To find the vertex of a parabola in standard form: Calculate the x-coordinate using the formula Substitute this value into the original function to calculate the y-coordinate Determine the value of the vertex and graph using the calculator. 1. 2.

8
Quadratic Functions and Their Graphs An object is thrown upward from the top of a 100- foot cliff. Its height in feet above ground after t seconds is given by the function f(t) = -16t 2 +10t +100. Find the maximum height of the object and the number of seconds it took for the object to reach its maximum height. Minimum/Maximum is the VERTEX After 5/16ths of a second, the object reaches its maximum height of 101 and 9/16 feet. Section 11.6

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google