Question

Which equation matches the graph shown below?

Answer 1

The graph is a parabola with roots at (-4.5, 0) and (0.5, 0) and vertex at (-2, -13)
Equation using roots is a(x + 9/2)(x - 1/2) = a(x^2 + 4x - 9/4) = ax^2 + 4ax - 9/4 a . . . . . . . . (1)
Equation using vertex is a(x + 2)^2 - 13 = a(x^2 + 4x + 4) - 13 = ax^2 + 4ax + 4a - 13 . . . . . . . . (2)
From (1) and (2), -9/4 a = 4a - 13
13 = 4a + 9/4 a = 25/4 a
a = (4 x 13)/25 = 2.08 = 2 approx

Therefore required equation is y = 2x^2 + 4(2)x + 4(2) - 13 = 2x^2 + 8x + 8 - 13 = 2x^2 + 8x - 5