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

Explanation:

Step1: Find the roots of the function

Set (f(x) = 0), then (-(x + 9)(x - 21)=0). By the zero - product property, (x+9 = 0) gives (x=-9), and (x - 21=0) gives (x = 21).

Step2: Use the formula for the axis of symmetry of a quadratic function in factored form

For a quadratic function (y=a(x - r_1)(x - r_2)), the axis of symmetry is (x=\frac{r_1 + r_2}{2}). Here (r_1=-9) and (r_2 = 21), so (x=\frac{-9+21}{2}). Calculate (\frac{-9 + 21}{2}=\frac{12}{2}=6).

Answer:

(x = 6) (corresponding to the third option)