27)

 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. what is the standard form of the equation?

a)the vertex form of the equation is f(x) = (x + 5)2 + 8. the standard form of the equation is f(x) = x2 + 10x + 33.
b)the vertex form of the equation is f(x) = (x - 5)2 + 8. the standard form of the equation is f(x) = x2 - 10x + 33.
c)the vertex form of the equation is f(x) = −(x + 5)2 + 8. the standard form of the equation is f(x) = x2 - 10x + 33.
d)the vertex form of the equation is f(x) = (x + 5)2 - 8. the standard form of the equation is f(x) = −x2 + 10x - 33.

A, The vertex form of the equation is f(x) = (x + 5)² + 8. The standard form of the equation is f(x) = x² + 10x + 33

Step-by-step explanation:

the vertex form is, as you stated: a(x - h)² + k, where (h,k) is the vertex of the parabola

we are given the vertex (-5,8), so we plug in these values into the equation:

(x + 5)² + 8 (positive 5 on the inside because we are given a -5 and the original equation has a negative on the inside)

to get it into standard form, we can FOIL out (x+5)² to expand the equation, and that gives us:

x² + 10x + 25

now we add 8 to 25 because we cant forget that

x² + 10x + 33 is our equation, meaning the answer is A

898.1666667

step-by-step explanation:

5389/6 = 898.1666667