Start with the equation of a vertical parabola: y-k = a(x-h)^2. We are told that the coordinates of the vertex are -1 and -8. Substituting these into the above equation,
y-[-8] = a(x-[-1]), or y+8 = a(x+1)^2. The coefficient a is undetermined here. How do we find it?
At any root, y=0, as a "root" is a point at which the graph crosses the x-axis.
Thus, if we choose to work with the given root 1, the associated point is (1,0). Substitute these coordinates into the above equation y+8 = a(x+1)^2.
We get 0+8 = a(1+1)^2, or 8 = a(2)^2, or 8 = 4a, or a = 2.
Substituting this value for a into the above equation,
y+8 = 2(x+1)^2.
You should check this result by determining whether the other root (-3,0) satisfies this equation. If yes, then you'll know for certain that this equation correctly describes the parabola in question.
