02Atransformquads

toc = **Transformations and the Parabola** =

You should be familiar with applying transformations such as dilations, translations and reflections when sketching a parabola from a quadratic equation that is in turning point form.

** Example 1 **
State the changes required to transform the graph of y = x 2 into the graph of the following. a) y = 4x 2 + 3
 * Dilation by a factor of 4 in the y-direction (or from the x-axis).
 * Translation 3 units up (in the y-direction).

b) y = – ½ (x + 3) 2
 * Dilation by a factor of ½ in the y-direction.
 * Reflection across the x-axis (inverted)
 * Translation by 3 units to the left.



** Example 2 **
Use transformations to find the equation of the graph shown.

tp is at (–3, 8) and graph is inverted so equation is in the form: y = –a(x + 3) 2 + 8

To find a: Graph passes through (–1, 0) 0 = –a(–1 + 3) 2 + 8 a(2) 2 = 8 4a = 8 a = 2 Hence equation is y = –2(x + 3) 2 + 8

** Demonstration **
To view an interactive demonstration of parabolas in turning point form, go here.

** Questions **
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