Question

The parabola passes through coordinates left parenthesis negative 5 comma negative 6 right parenthesis, left parenthesis negative 4 comma 0 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis negative 1 comma 6 right parenthesis.

Write the equation of the graph in standard form.

(1 point)

y=x2−6x+8


y=−2x2−12x−18


y=2x2+12x+16


y=x2+6x+7

Answer 1

y = 2x^2 + 12x + 16

Reason: symmetry gives axis x = -3 and vertex (-3, -2), so y = a(x+3)^2 - 2. Using (-4,0): 0 = a(1)^2 - 2 ⇒ a = 2, so y = 2(x+3)^2 - 2 = 2x^2 + 12x + 16.