# g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. g(x) = -1/4 (x + 2)^2 - 2

g is related to one of the parent functions described in Section 1.6. Describe the sequence of transformations from f to g. $$\displaystyle{g{{\left({x}\right)}}}=-\frac{{1}}{{4}}{\left({x}+{2}\right)}^{{2}}-{2}$$

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We are starting with the parent function $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}$$
SETP 1: Vertically compress the graph by a factor of 2/3, to get $$\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}$$
STEP 2: Shift the graph by 4 units up, to get $$\displaystyle{y}={\left(\frac{{2}}{{3}}\right)}{x}^{{2}}+{4}$$, which is the required function g(x)