What is the equation for , vertex (-4,-1) and point (-6,-13)

I think this must be a parabola we are dealing with. The general form of a parabola in vertex form is:

y = a(x - h)² + k, where (h, k) is the vertex.

 

We know the vertex...h = -4, and k = -1

y = a(x + 4)² - 1

 

We know x = -6 and y = -13 makes the equation true. So plug these in and solve for a.

-13 = a(-6 + 4)² - 1

-12 = a(-2)²

-12 = 4a

-3 = a

 

Now we know h, k, and a. So the equation is:

y = -3(x + 4)² - 1