# Question #37497

Jan 20, 2018

See explanation.

#### Explanation:

Begin with the graph of $f \left(x\right) = {x}^{2}$.

$g \left(x\right)$ is created by a series of transformations to that graph.

$g \left(x\right) = - {\left(x - 4\right)}^{2} + 5$:

Take the graph of $f \left(x\right)$ and shift it 4 units to the right to get a graph of $y = {\left(x - 4\right)}^{2}$.

Now take your new graph and reflect it over the $x$-axis to get the graph of $y = - {\left(x - 4\right)}^{2}$.

Take this new graph and shift it up 5 units to get the graph of $y = - {\left(x - 4\right)}^{2} + 5$, which is the graph of $g \left(x\right)$.