Question

# Describe the transformations that were applied to y=x^{2} to obtain each of the following functions y=-2(x-1)^{2}+23\ and y=(\frac{12}{13}(x+9))^{2}-14\

Transformations of functions

Describe the transformations that were applied to $$\displaystyle{y}={x}^{{{2}}}$$ to obtain each of the following functions.

$$\displaystyle{a}{)}{y}=-{2}{\left({x}-{1}\right)}^{{{2}}}+{23}\$$

$${b}{)}{y}={\left({\frac{{{12}}}{{{13}}}}{\left({x}+{9}\right)}\right)}^{{{2}}}-{14}\$$

$${c}{)}{y}={x}^{{{2}}}-{8}{x}+{16}\$$

$${d}{)}{y}={\left({x}+{\frac{{{3}}}{{{7}}}}\right)}{\left({x}+{\frac{{{3}}}{{{7}}}}\right)}\$$

$${e}{)}{y}={40}{\left(-{7}{\left({x}-{10}\right)}\right)}^{{{2}}}+{9}$$

2021-07-31
Step 1
Describe the transformed function for the original equation is $$\displaystyle{y}={x}^{{{2}}}$$ for the following terms:
$$\displaystyle{\left({a}\right)}{y}=-{2}{\left({x}-{1}\right)}^{{{2}}}+{23}$$
$$\displaystyle{a}=-{2}\ {k}={1}\ {d}={1}\ {c}={23}$$
$$\displaystyle{\left({b}\right)}{y}={\left[{\frac{{{12}}}{{{13}}}}{\left({x}+{9}\right)}\right]}^{{{2}}}-{14}$$
$$\displaystyle{k}={\frac{{{12}}}{{{13}}}}\ {d}=-{9}\ {c}=-{14}$$
$$\displaystyle{\left({c}\right)}{y}={x}^{{{2}}}-{8}{x}+{16}$$
$$\displaystyle={\left({x}-{4}\right)}^{{{2}}}$$
$$\displaystyle{d}={4}$$
$$\displaystyle{\left({d}\right)}{y}={\left({x}+{\frac{{{3}}}{{{7}}}}\right)}{\left({x}+{\frac{{{3}}}{{{7}}}}\right)}$$
$$\displaystyle={\left({x}+{\frac{{{3}}}{{{7}}}}\right)}^{{{2}}}$$
$$\displaystyle{d}=-{\frac{{{3}}}{{{7}}}}$$
$$\displaystyle{\left({e}\right)}{y}={40}{\left[-{7}{\left({x}-{10}\right)}\right]}^{{{2}}}+{9}$$
$$\displaystyle{a}={40}\ {k}=-{7}\ {d}={10}\ {c}={9}$$