Question

find the equation of the quadratic function with roots -8 and -6 and vertex at (-7,-3)

Answer 1

The vertex is (h,k) = (-7,-3)

So
\[\Large y = a(x-h)^2 + k\]
turns into
\[\Large y = a(x-(-7))^2 + (-3)\]
\[\Large y = a(x+7)^2 - 3\]

Answer 2

Plug in one of the x-intercepts, say (-8,0) in for x and y

\[\Large y = a(x+7)^2 - 3\]
\[\Large 0 = a(-8+7)^2 - 3\]
now solve for 'a' and tell me what you get