Download presentation

Presentation is loading. Please wait.

Published byAlbert Walters Modified over 4 years ago

1
Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

2
All quadratic functions are parabolas: “U” shaped Standard form: y = ax 2 + bx + c If a is positive, the graph opens up If a is negative, the graph opens down Always have a vertex that is either the maximum or minimum If the parabola opens up, it has a minimum If the parabola opens down, it has a maximum Always have one y-intercept, which is at (0, c)

3
Determine the y-intercept and whether the graph opens up or opens down y = x 2 + 8x – 1 Opens: y-intercept: y = - 1 / 2 x 2 + 2 Opens: y-intercept: y = 2x 2 – x Opens: y-intercept: (0, -1) (0, 2) (0, 0) Up Down

4
In standard form, the axis of symmetry is found by using the equation: Take the number in front of the “x” (that’s “b”) and the number in front of the “x 2 ” (that’s “a”), and plug them into the equation above.

5
Example: For the equation: y = x 2 – 2x – 3 find the axis of symmetry So x= The axis of symmetry also is the first step in finding the vertex of a parabola a = 1, b = -2, c = -3

6
The vertex of a parabola is located at: This means that: The x-coordinate is at –b / 2a The y-coordinate is the number you get when you plug the x-value back into the original function. Example In the graph: y = x 2 – 2x – 3, find the vertex. We know x = 1 (last slide), so substitute 1 in for x and solve. y = (1) 2 – 2(1) – 3 = -4 The vertex is at (1, -4)

7
Find the axis of symmetry and the vertex y = -x 2 + 4x + 3 Axis of symmetry: Vertex: y = - 1 / 3 x 2 – 2x – 4 Axis of symmetry: Vertex: x = 2 x = -3 (2, 7) (-3, -1)

8
Assignment Page 248 Problems 1-21, odd I GNORE THE DIRECTIONS !!! Tell me: a) Whether the graph opens up or opens down b) The y-intercept c) The axis of symmetry d) The vertex

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