Question

A parabola has a vertex at (-6, 6) and roots at 10 and m. Find the value of m.

Answer 1

Answer:

m = -22

Step-by-step explanation:

Formula for parabola in it's vertex form is given by;

y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex.

We are told that vertex is at (-6, 6) and the roots are at 10 and m.

Thus;

y = a(x - (-6))² + 6

y = a(x + 6)² + 6

Since 10 is a root, thus;

0 = a(10 + 6)² + 6

-6 = 256a

a = -6/256

a = -3/128

Thus,the equation is;

y = (-3/128)(x + 6)² + 6

Since m is a root, then;

0 = (-3/128)(m + 6)² + 6

-6 = (-3/128)(m + 6)²

Rearranging, we have;

128 × 6/3 = (m + 6)²

256 = m² + 12m + 36

m² + 12m - 256 + 36 = 0

m² + 12m - 220 = 0

Using quadratic formula, we have;

m = 10 or -22