Determine the equation for the parabola graphed below.

The generic equation of a parabola is:
 f (x) = ax ^ 2 + bx + c
 To verify the equation of the parabola you need three points:
 f (x) = ax ^ 2 + bx + c
 We choose the points:
 (x, y) = (- 1,7)
 7 = a (-1) ^ 2 + b (-1) + c
 7 = a - b + c
 (x, y) = (0,5)
 5 = a (0) ^ 2 + b (0) + c
 5 = c
 (x, y) = (- 2,5)
 5 = a (-2) ^ 2 + b (-2) + c
 5 = 4a - 2b + c
 We solve:
 c = 5
 5 = 4a - 2b + 5
 7 = a - b + 5
 Rewriting
 b = 2a
 a-b = 2
 Substituting:
 a-2a = 2
 a = -2
 b = -4
 The equation of the parabola is:
 f (x) = - 2x ^ 2 -4x + 5