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