write an equation for the parabola with vertex: (-4,-5) and point (-6,-9)

Question

This is a question in my math study guide, and the teacher won't explain it.

Answer 1

f(x) = a(x - h)² + k

f(x) = a(x + 4)² - 5 insert the vertex

-9 = a(-6 + 4)² - 5 insert point

-4 = a(-2)²

-4 = 4a

-1 = a

f(x) = -(x + 4)² - 5

Answer 2

Start with vertex form for a parabola: y = a(x - h)² + k. The vertex (-4, -5) can be plugged in as (h, k) so that we have y = a(x + 4)² - 5. We don't know what a is, but if we plug in the other point we were given (-6, -9) as x and y, we will be able to solve for a:

-9 = a(-6 + 4)² - 5

-9 = 4a - 5

a = -1

Now we can plug h, k, and a into the vertex form: y = -(x + 4)² - 5 is the answer!