1 / 17

The vertex of the parabola is at ( h , k ).

The vertex of the parabola is at ( h , k ). Vertex form of a quadratic can be used to determine transformations of the quadratic parent function. Quadratic parent function: f(x) = x 2. Horizontal Translations: If f(x) = (x – 2) 2 t hen for (x – h) 2 ,( x – (2)) 2 , h = 2.

eden-richardson
Télécharger la présentation

The vertex of the parabola is at ( h , k ).

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The vertex of the parabola is at (h, k).

  2. Vertex form of a quadratic can be used to determine transformations of the quadratic parent function. Quadratic parent function: f(x) = x2

  3. Horizontal Translations: If f(x) = (x – 2)2 then for (x – h)2 ,(x – (2))2, h = 2. The graph moves two units to the right.

  4. Horizontal Translations: If f(x) = (x + 3)2 then for (x – h)2 ,(x – (-3))2 , h = -3 The graph moves three units to the left.

  5. Vertical Translations: If f(x) = (x)2 + 2 then for (x – h)2 + k, (x)2 + 2, k = 2 The graph moves two units up.

  6. Vertical Translations: If f(x) = (x)2 – 1 then for (x – h)2 + k, (x)2 – 1, k = -1 The graph moves one unit down.

  7. Horizontal and Vertical Translations: If f(x) = (x – 3)2 + 1 then for (x – h)2 + k, (x – (3))2 + 1, h = 3 and k = 1 The graph moves three units right and 1 unit up.

  8. Horizontal and Vertical Translations: If f(x) = (x + 1)2 – 2 then for (x – h)2 + k, (x – (-1))2 – 2, h = -1 k = -2 The graph moves one unit left and two units down.

  9. Horizontal and Vertical Translations: The vertex of a parabola after a translation is located at the point (h, k). If f(x) = (x + 7)2 + 3 then for (x – h)2 + k, (x – (-7))2+ 3, h = -7 k = 3. The translated vertex is located at the point (-7, 3).

  10. Reflection: If a is positive, the graph opens up. If a is negative, the graph is reflected over the x-axis.

  11. Vertical Stretch/Compression: The value of a is not in the parenthesis: a(x)2. If |a| > 1, the graph stretches vertically away from the x-axis. If 0 < |a| < 1, the graph compresses vertically toward the x-axis. f(x) = 2x2 , a = 2, stretch vertically by factor of 2.

  12. Horizontal and Vertical Stretch/Compression: Create a table of values of a horizontal and vertical stretch and compression.

  13. a = 2

  14. HW pg. 320 #’s 23-28, 31, 33-41, 45

More Related