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