Question

The zeros of a parabola are -4 and 2, and (6, 10) is a point on the graph. Which equation can be solved to determine the value of a in the equation of the parabola?

A) 6 - a(10 - 4)(10 + 2).
B) 6 - a(10 + 4)(10 - 2).
C) 10 - a(6 - 4)(6 + 2).
D) 10 - a(6 + 4)(6 - 2).

Answer 1

To determine the value of a in the equation of the parabola, we can use the fact that the zeros of the parabola are -4 and 2, and the point (6, 10) is on the graph. The equation that can be solved to determine the value of a is B) 6 - a(10 + 4)(10 - 2).

Step-by-step explanation:

To determine the value of a in the equation of the parabola, we can use the fact that the zeros of the parabola are -4 and 2, and the point (6, 10) is on the graph.

We can start by setting up the equation of the parabola in the vertex form, y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. Since the zeros are -4 and 2, the vertex must be the midpoint between -4 and 2, which is -1.

So the equation of the parabola is y = a(x+1)^2 + k.

Plugging in the point (6, 10), we get 10 = a(6+1)^2 + k. Now we can solve for a by substituting the known values: 10 = a(7)^2 + k.

Simplifying this equation gives us the equation B) 6 - a(10 + 4)(10 - 2).