Question

what is the value of $a$ in this functions equation?
a. -2
b. 1
c. -1
d. 2

Explanation:

Step1: Identify vertex form

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

Step2: Use a point to solve for $a$

The parabola passes through $(2, 4)$. Substitute $x=2, y=4$:
$4 = a(2)^2 + 8$

Step3: Simplify and solve for $a$

$4 = 4a + 8$
$4a = 4 - 8 = -4$
$a = \frac{-4}{4} = -1$

Answer:

C. -1