Download presentation

Presentation is loading. Please wait.

Published byJake Stoner Modified over 2 years ago

1
Essential Question(s): How can you tell if a quadratic function a) opens up or down b) has a minimum or maximum, and c) how many x-intercepts it has?

2
“Wait… didn’t we do this already?” I tried to warn you… The notes that follow in yellow, I will expect you to memorize (meaning: they won’t be given to you on a quiz) Quadratic Functions are parabolas (‘U’ shaped) and a) Can open either upward or downward b) Always have a vertex which is either the maximum or minimum Opening up == minimum, opening down == maximum c) Always have exactly one y-intercept d) Can have 0, 1, or 2 x-intercepts The x-intercept(s) are the solution(s) [roots] of the equation

3
Quadratic Functions can be written in one of three forms Transformation form: f (x) = a(x – h) 2 + k Most useful for finding the vertex of a parabola Vertex is at (h, k) (Set inside parenthesis = 0 & solve, number outside) If a is positive, the graph opens up. If a is negative, graph opens down. The y-intercept is at ah 2 + k The x-intercepts are at

4
Using Transformation Form Find the vertex of the function and state whether the graph opens upward or downward g(x) = -6(x – 2) 2 – 5 h(x) = -x 2 + 1 h = 2 and k = -5, so vertex is at (2, -5) Because a = -6, graph opens down There is no h, and k = 1 so vertex is at (0, 1) Because a = -1, graph opens down

5
Polynomial form: f (x) = ax 2 + bx + c Yeah, we’ve seen this plenty already… Most useful for finding the y-intercept y-intercept is at (0, c) If a is positive, the graph opens up. If a is negative, graph opens down. The vertex is at The x-intercepts are at

6
Using Polynomial Form Determine the y-intercept and state whether the graph opens upward or downward g(x) = x 2 + 8x – 1 g(x) = 2x 2 – x + 5 The y-intercept is at (0, -1) Because a = 1, graph opens up The y-intercept is at (0, 5) Because a = 2, graph opens up

7
x-intercept form: f (x) = a(x – s)(x – t) This is simply polynomial form factored out Most useful for finding the x-intercepts (duh) x-intercepts are at (s, 0) and (t, 0) If a is positive, the graph opens up. If a is negative, graph opens down. The vertex is at The y-intercepts is at (0, ast)

8
Using x-intercept Form Determine the x-intercepts and state whether the graph opens upward or downward h(x) = -2(x + 3)(x + 1) f(x) = -0.4(x + 2.1)(x – 0.7) The x-intercept are at (-3, 0) and (-1, 0) Because a = -2, graph opens down The x-intercepts are at (-2.1, 0) and (0.7, 0) Because a = -0.4, graph opens down

9
Assignment Page 170 Problems 1-25, odd problems

Similar presentations

OK

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on security features of atm machine Ppt on credit default swaps charts Making a ppt on ipad Ppt on history of music Ppt on sound navigation and ranging system sensor Ppt on limits and derivatives definition Ppt on mid day meal programme Ppt on biography of albert einstein Ppt on motivation and leadership Ppt on advanced construction materials and techniques