Answer:
Since the given quadratic function has zeros of -8 and 4, we know that the factors of the quadratic equation are (x + 8) and (x - 4).
The maximum of the function occurs at the midpoint between the zeros, which is (-8 + 4)/2 = -2. So, the x-coordinate of the vertex is -2.
We also know that the y-coordinate of the vertex is 18. So, the vertex of the quadratic function is (-2, 18).
Using the vertex form of the quadratic function, we can write:
F(x) = a(x + 2)^2 + 18
Since the function has zeros of -8 and 4, we can write:
F(x) = a(x + 8)(x - 4)
a(x + 2)^2 + 18 = a(x + 8)(x - 4)
ax^2 + 6ax - 128a - 576 = ax^2 + 16ax - 32a
10ax - 96a - 576 = 0
10a(x - 6) = 0
a = 0 or x = 6.
Since the vertex is a maximum and the coefficient of the x^2 term is positive, we know that a > 0. Therefore, we can conclude that x = 6 and a = 3.
Hence, the value of "a" in the function equation is 3.