what is the value of $a$ in this functions equation?\na. -2\nb. 1\nc. -1\nd. 2

Explanation:

Step1: Identify vertex form

The parabola has vertex at $(0, 8)$, so its equation is $y = ax^2 + 8$.

Step2: Substitute a known point

Use the x-intercept $(2, 0)$: $0 = a(2)^2 + 8$

Step3: Solve for a

Simplify and isolate $a$: $4a = -8$ $a = \frac{-8}{4} = -2$

Answer:

A. -2