# Describe the transformations that must be applied to y=x^2 to create the graph of each of the following functions. a) y=1/4(x-3)^2+9b) y=((1/2)x)^2-7

Describe the transformations that must be applied to $y={x}^{2}$ to create the graph of each of the following functions.
a) $y=\frac{1}{4}{\left(x-3\right)}^{2}+9$
b) $y={\left(\left(\frac{1}{2}\right)x\right)}^{2}-7$

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To create the graph of the function a) $y=\frac{1}{4}{\left(x-3\right)}^{2}+9$
We have (by the function)
1. vertical compression by $\frac{1}{4}$
2. horizontal translation 3 units to the right
3. vertical translation 9 units up
b) $y={\left(\left(\frac{1}{2}\right)x\right)}^{2}-7={\left(\left(\frac{1}{4}\right)x\right)}^{2}-7$
1. vertical compression by $\frac{1}{4}$
2. vertical translation 7 units down