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Q. 9

Expert-verifiedFound in: Page 155

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.

The given statement is:

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

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" $f\left(2\right)$.

The given statement is true.

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