37.5k views
2 votes
What is the equation of the quadratic function with roots -3 and 1 and a vertex a (-1, -8)?

User LeeJB
by
7.6k points

1 Answer

3 votes
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.
User Marguerita
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.