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
