Let the equation be:
y = ax^2 + bx + c.
Then, substitue the three points into the equation.
First point: 0 = a0^2 + b0 + c.
So c = 0.
Second point: -2 = a(-1)^2 + b(-1) + c.
So a - b + c = -2.
Third point: 6 = a*1^2 + b*1 + c.
So a + b + c = 6.
We know that c=0 already, so we substitute c=0 into the last two equations and we would get:
a - b = -2
a + b = 6
We add the two equations and we get:
2a = 4
a = 2
Then, we substitute a=2 into a-b=-2 and we get:
-b = -4
b = 4
Now we know a = 2, b = 4, and c = 0
Then, the equation of the parabola would be:
2x^2 + 4x
