Find the vertex equation form,f(x)=a(x-h)^2+k,for a parabola that passes through the point(-6,9)and has(-5,8)as it’s vertex.what is the standard form of the equation

y = 1(x+5)^2 + 8  and  y = x^2 + 10x + 33

Step-by-step explanation:

Find the vertex equation form (f(x)=a(x-h)^2+k for a parabola that passes through the point (-6,9) and has (-5,8) as its vertex.

First, substitute the given coordinates of the vertex into this equation:

f(x) = a(x+5)^2 + 8.

Next, subst. the coordinates of the point (-6, 9) into the above:

9 = a(-6+5)^2 + 8, or 9 = a + 8.  Then a = 1.

We thus have the vertex equation y = 1(x+5)^2 + 8.

What is the standard form of the equation?  Expand the vertex equation as follows:  y = x^2 + 10x + 25 + 8, or y = x^2 + 10x + 33