Question

The parabola grows through left parenthesis negative 8.5 comma negative 3 right parenthesis, peaks at left parenthesis negative 4 comma 2 right parenthesis, then drops to left parenthesis negative 0.5 comma negative 4 right parenthesis. All values are approximate.

Which response is the correct way to write the equation in vertex form for the function?

(1 point)

y=−1/4(x−2)2+4


y=−1/4(x+2)2+4


y=−1/4(x−4)2+2


y=−1/4(x+4)2+2

Answer 1

y = −1/4(x + 4)^2 + 2

Reason: the vertex is (−4, 2) so the form is y = a(x + 4)^2 + 2, and because the graph has a maximum a < 0. Using (−8.5, −3): −3−2 = a(−8.5+4)^2 → −5 = a(4.5)^2 → a ≈ −5/20.25 ≈ −0.247 ≈ −1/4.