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Q. 9

Expert-verified
Found in: Page 155

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# True or False The y-coordinate of the vertex of $f\left(x\right)=-{x}^{2}+4x+5$ is $f\left(2\right)$.

The given statement is true.

See the step by step solution

## Step 1. Given information.

The given statement is:

The y-coordinate of the vertex of $f\left(x\right)=-{x}^{2}+4x+5$ is $f\left(2\right)$.

## Step 2. Determine whether the given statement is true or false.

The vertex of $f\left(x\right)=a{x}^{2}+bx+c$ is $\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)$.

In the given function $f\left(x\right)=-{x}^{2}+4x+5,a=-1,b=4,c=5$.

$\begin{array}{rcl}-\frac{b}{2a}& =& -\frac{4}{2\left(-1\right)}\\ & =& -\frac{4}{-2}\\ & =& 2\end{array}$

The y-coordinate of the vertex of the given function is role="math" localid="1645862681108" $f\left(2\right)$.

## Step 3. Conclusion.

The given statement is true.