Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Vertex form of a quadratic can be used to determine transformations of the quadratic parent function.

Quadratic parent function: f(x) = x2

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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.

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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.

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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 + 3then for (x – h)2 + k, (x – (-7))2 + 3, h = -7 k = 3.The translated vertex is located at the point (-7, 3).

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Reflection:If a is positive, the graph opens up.

If a is negative, the graph is reflected over the x-axis.

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

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.

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Horizontal and Vertical Stretch/Compression:

Create a table of values of a horizontal and vertical stretch and compression.

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

Vertical Stretch: f(x) = 2x2

x f(x)

1 2(1)2 = 2

2 2(2)2 = 8

3 2(3)2 = 18

Hor. Compress: f(x) = (2x)2

x f(x)

1 (2∙1)2 =4

2 (2∙2)2 = 16

3 (2∙3)2 =81

a = 2

Holt Algebra 2

5-1 Using Transformations to Graph Quadratic Functions

HW pg. 320

#’s 23-28, 31, 33-41, 45