Question

what is the axis of symmetry of the function $f(x)=-(x+9)(x-21)$?
$x=-15$
$x=-6$
$x=6$
$x=15$

Explanation:

Step1: Find the x-intercepts

Set $f(x)=0$, solve $-(x+9)(x-21)=0$.
The x-intercepts are $x=-9$ and $x=21$.

Step2: Calculate midpoint of intercepts

Axis of symmetry is the average of the two intercepts.
$\text{Axis of symmetry} = \frac{-9 + 21}{2}$

Step3: Compute the value

$\frac{-9 + 21}{2} = \frac{12}{2} = 6$

Answer:

C. $x=6$