Chapter 2, Problem 1RE

Given $f\left(x\right)=-{\left(x+5\right)}^2+2,$ identity the vertex of the graph of the parabola.

To determine

To calculate: The vertex of the graph of the parabola $f\left(x\right)=-{\left(x+5\right)}^2+2$ .

Answer to Problem 1RE

The vertex of the given parabola is $\left(-5,2\right)$ .

Explanation of Solution

Calculation:

Consider the given equation as $f\left(x\right)=-{\left(x+5\right)}^2+2$ .

The vertex of the graph of the parabola $f\left(x\right)=a{(x-h)}^2+k$ is given as $\left(h,k\right)$ .

Now, compare the given equation with the general form $f\left(x\right)=a{(x-h)}^2+k$ as,

$\begin{array}{c}f\left(x\right)=-{\left(x+5\right)}^2+2\\ =-{\left[x-\left(-5\right)\right]}^2+2\end{array}$

It can be observed from the above equation that $h=-5$ and $k=2$ .

Therefore, the vertex of the given parabola is $\left(-5,2\right)$ .