Question

What is the axis of symmetry of the function f(x)=−(x+9)(x−21)? x=−15 x=−6 x=6 x=15

Answer 1

Answer: The axis of symmetry of a quadratic function in the form f(x) = a(x-h)^2 + k is x = h. To find the axis of symmetry of the function f(x) = -(x+9)(x-21), we first need to rewrite it in the form of f(x) = a(x-h)^2 + k by using the distributive property of multiplication:

f(x) = -(x+9)(x-21)

f(x) = -x(x-21) - 9(x-21)

f(x) = -x^2 + 21x - 9x + 189

f(x) = -x^2 + 12x + 189

Now we can see that h = -b/2a = -12/(2*(-1)) = 6. So the axis of symmetry of the function is x = 6. Therefore, the answer is x=6.

Explanation: