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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.

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

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  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

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