what is the axis of symmetry of the function f(x)=-(x + 9)(x - 21)?\no x=-15\no x=-6\no x=6\no x=15

Explanation:

Step1: Identify the x - intercepts

The x - intercepts of the function $f(x)=-(x + 9)(x - 21)$ are found by setting $f(x)=0$. So $x+9 = 0$ gives $x=-9$ and $x - 21=0$ gives $x = 21$.

Step2: Use the axis - of - symmetry formula

The axis of symmetry of a quadratic function in factored form $y=a(x - p)(x - q)$ is $x=\frac{p + q}{2}$. Here $p=-9$ and $q = 21$. Then $x=\frac{-9+21}{2}$.

Step3: Calculate the value of x

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

Answer:

C. $x = 6$