Download presentation

Published byLoren Fitchett Modified over 4 years ago

1
Quadratic graphs Today we will be able to construct graphs of quadratic equations that model real life problems

2
**The Graph of a Quadratic Function**

All parabolas are symmetric with respect to a line called the axis of symmetry. The point where the axis intersects the parabola is the vertex of the parabola. The Graph of a Quadratic Function Leading coefficient is positive. Leading coefficient is negative.

3
**The leading coefficient of ax2 + bx + c is a.**

y a > 0 opens upward When the leading coefficient is positive, the parabola opens upward and the vertex is a minimum. f(x) = ax2 + bx + c vertex minimum x y vertex maximum When the leading coefficient is negative, the parabola opens downward and the vertex is a maximum. f(x) = ax2 + bx + c a < 0 opens downward Leading Coefficient

4
**Axis of symmetry Formula for:**

We can also trace to it on the graphing calculator!

5
**The vertex of the graph of f (x) = ax2 + bx + c (a 0)**

Vertex of a Parabola The vertex of the graph of f (x) = ax2 + bx + c (a 0) Example: Find the vertex of the graph of f (x) = x2 – 10x + 22. f (x) = x2 – 10x original equation a = 1, b = –10, c = 22 At the vertex, So, the vertex is (5, -3). Vertex of a Parabola

6
**Find the maximum height of the ball.**

Example: A basketball is thrown from the free throw line from a height of six feet. What is the maximum height of the ball if the path of the ball is: The path is a parabola opening downward. The maximum height occurs at the vertex. Find the maximum height of the ball. Example: Basketball

7
**The maximum height of the ball is 15 feet.**

Example: A basketball is thrown from the free throw line from a height of six feet. What is the maximum height of the ball if the path of the ball is: The path is a parabola opening downward. The maximum height occurs at the vertex. At the vertex, So, the vertex is (9, 15). The maximum height of the ball is 15 feet. Example: Basketball

8
**Graph the following path of a ball**

Y=-x2+6x Find the Max height After how Seconds does the ball hit the ground.

9
**Plot the points 10 8 6 4 2 0 2 4 6 8 10 Max height is 9**

H E I G T The ball hits the ground After 6 seconds SECONDS

10
**THINGS TO KEEP IN MIND WHEN GRAPHING**

CHANGE THE VIEWING WINDOW BY CHANGING THE Y MIN AND Y MAX. REMEMBER THAT HEIGHT IS THE VERTICAL AXIS AND TIME IS THE HORIZONTAL AXIS

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