Question

# 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

Transformations of functions
h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
$$\displaystyle{h}{\left({x}\right)}=\frac{{1}}{{2}}{\left({x}−{1}\right)}^{{2}}−{2}$$

2021-06-12

We are starting with the parent function $$f(x) = x^2$$

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

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

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