Download presentation

Presentation is loading. Please wait.

Published byLogan Goodman Modified over 6 years ago

1
ParabolasParabolas by Dr. Carol A. Marinas

2
Transformation Shifts Tell me the following information about: f(x) = (x – 4) 2 – 3 What shape is the graph? What direction is it going? What is the vertex? Is it a high point or low point? What is the y-intercept?

3
Transformation Shifts Tell me the following information about: f(x) = (x – 4) 2 – 3 What shape is the graph? parabola What direction is it going? up What is the vertex? (4, –3) Is it a high point or low point? Low point What is the y-intercept? (0, 13)

4
y =(x – 4) 2 – 3

5
Standard Form y = (x – h) 2 + k Vertex is (h, k) Line of Symmetry is x = h

6
Standard to General Form y =(x – 4) 2 – 3 y = (x 2 – 8x + 16) – 3 y = x 2 – 8x + 13

7
General to Standard Form y = x 2 – 8x + 13 y – 13 = x 2 – 8x y – 13 + 16 = x 2 – 8x + 16 y + 3 = (x – 4) 2 y = (x – 4) 2 – 3 Vertex is (4, – 3) Get ‘a’ equal to 1 by multiplying or dividing the equation. (done) Move constant to left side Complete the square Solve for y

8
General Form y = ax 2 + bx + c Vertex is ( –b/2a, f(–b/2a) ) y-intercept is (0, c) Line of Symmetry is x = –b/2a Example: y = x 2 – 8x + 13 Vertex is ( –(– 8)/2(1), f (8/2)) or (4, f(4)) or (4, –3) y-intercept is (0, 13) Line of Symmetry is x = 4

9
x-intercepts For x-intercepts, the y value is 0. y = ax 2 + bx + c becomes 0 = ax 2 + bx + c which is a quadratic equation that is solved by factoring or the quadratic formula.

10
x-intercepts using Quadratic Formula 0 = ax 2 + bx + c x = b 2 – 4ac is the discriminant and is used to tell us how many x-intercepts exist.

11
Discriminant if less than 0, no x-intercepts b 2 – 4ac if it is 0, 1 x-intercept if greater than 0, 2 x-intercepts Example: y = x 2 – 8x + 13 The discriminant is (–8) 2 – 4(1)(13) or 64 – 52 or 12 Since 12 > 0, there are 2 x-intercepts.

12
Finding the x-intercepts Ex: y = x 2 – 8x + 13 The discriminant is 12. To actually find the x-intercepts, let’s continue using the Quadratic Formula. x = = x = 8 ± √12 = 8 ± 2√3 = 4 ± 2 2 The x-intercepts are (4 –, 0 ) and (4 +, 0)

13
Final Graph of y = (x – 4) 2 – 3 or y = x 2 – 8x + 13

14
ReviewReview Standard Form y = (x – h) 2 + k General Form y = ax 2 + bx + c Know how to find the following: * Vertex * y-intercept(s) * High/Low Point * x-intercept(s) * Axis of Symmetry * Graph the parabola

Similar presentations

© 2021 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