Question

Suppose a parabola has an axis of symmetry at x = –7 , a maximum height of 4 and also passes through the point (–6, 0). Write the equation of the parabola in vertex form.

Answer 1

what does maximum height of a parabola refer to?

Answer 2

ahh finally one of these that does not have too much information
you are being told in a round about way what the vertex is. max is 4 when \(x=-7\) means the vertex is \((-7,4)\)

Answer 3

so you know it looks like \(y=a(x+7)^2+4\) you just don't know what \(a\) is.
however, you also know if \(x=-6\) then \(y=0\) so you can set
\[0=a(-6+7)^2+4\] and solve for \(a\)