Download presentation

Presentation is loading. Please wait.

Published byDouglas Fletcher Modified over 6 years ago

1
2.3 Quadratic Functions

2
A quadratic function is a function of the form:

3
Properties of the Graph of a Quadratic Function Parabola opens up if a > 0; the vertex is a minimum point. Parabola opens down if a < 0; the vertex is a maximum point.

4
a > 0 Opens up Vertex is lowest point Axis of symmetry Graphs of a quadratic function f(x) = ax 2 + bx + c a < 0 Opens down Vertex is highest point Axis of symmetry

5
Steps for Graphing a Quadratic Function by Hand Determine the vertex. Determine the axis of symmetry. Determine the y-intercept, f(0). Determine how many x-intercepts the graph has. If there are no x-intercepts determine another point from the y-intercept using the axis of symmetry. Graph.

6
Without graphing, locate the vertex and find the axis of symmetry of the following parabola. Does it open up or down? Vertex: Since -3 < 0 the parabola opens down.

7
Finding the vertex by completing the square:

8
(0,0) (2,4)

9
(0,0) (2, -12)

10
(2, 0) (4, -12)

11
(2, 13) Vertex

12
Determine whether the graph opens up or down. Find its vertex, axis of symmetry, y-intercept, x- intercept. x-coordinate of vertex: Axis of symmetry: y-coordinate of vertex:

13
There are two x-intercepts:

14
Vertex: (-3, -13) (-5.55, 0)(-0.45, 0) (0, 5)

Similar presentations

© 2022 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