Question

# 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

Transformations of functions
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

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