For homewok,terrys has to creat an equation of a parabola that has a vertex (-6,12) asn includs point (-10,0).She proceeds with the following steps.

Answer 1

Vertex = (-6, 12)

Point = (-10, 0)

If we recall the vertex form of a quadratic equation, we use it to solve this problem:

Vertex form:

f(x) = a(x - h)² + k *Plug in the information that is given. The vertex is in the form (h,k)

f(x) = a(x + 6)² + 12 *Now we plug in the point that we are given for x and f(x)

0 = a(-10 + 6)² + 12 * Solve for a

0 = a(-4)² + 12

0 = 16a + 12

-12 -12

-12 = 16a

a = -12/16

a = -3/4 (reduce your fraction)

*Now plug your "a" value back into the vertex form:

Answer: f(x) = -3/4(x + 6)² + 12

Hope this helps :)