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
ANSWERED
asked 2021-07-30

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

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

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

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

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

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

Answers (1)

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