Answer:
y = (x + 4.5)² - 13.25
Explanation:
y = x² + 9x + 7
We need to get a perfectly squared binomial as part of the right side.
Take the '9x' term, divide it in half, square it, add and also subtract it on the right side, as shown below. That would be (4.5)² = 20.25 added and subtracted.
y = x² + 9x + 7
y = x² + 9x + 20.25 + 7 - 20.25
y = (x² + 9x + 20.25) - 13.25
y = (x + 4.5)² - 13.25
y = (x + 4.5)² - 13.25
Vertex Form is y = a(x-h)² + k, where the parabola vertex is (h, k)
So if you wrote this as y = 1(x - [-4.5] )² + (-13.25), we would see that a = 1, and h = -4.5 and k = -13.25.
Vertex = (-4.5, -13.25)
I verified on a graphing calculator that this is indeed the vertex of the parabola.