h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h. h(x)=1/2(x−1)^2−2

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
$h\left(x\right)=\frac{1}{2}{\left(x-1\right)}^{2}-2$
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We are starting with the parent function $f\left(x\right)={x}^{2}$

STEP 1: Vertically compress the graph by a factor of 1/2, to get $y=\left(1/2\right){x}^{2}$

STEP 2: Shift the graph by 1 unit to the right, to get $y=1/2\left(x-1{\right)}^{2}$

STEP 3: Shift the graph by 2 units downwards, to get $y=1/2\left(x-1{\right)}^{2}\right)-2$, which is the required function h(x)

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