Algebra
posted by Eric .
Please help I can't figure out these two.
Express f(x) in the form a(x − h)2 + k.
f(x) = −4x2 + 24x − 9
Find the standard equation of a parabola that has a vertical axis and satisfies the given conditions.
vertex (0, −7), passing through (3, 38)
Thank You!

for the first, complete the square:
f(x) = 4(x^2  6x ......)  9
= 4( x^2  6x + 9 9)  9
= 4( (x3)^2  9)  9
= 4(x3)^2 + 36  9
= 4(x3)^2 + 27
for the second, you know the vertex is (0,7)
so f(x) = a(x0)^2  7
= ax^2  7
but (3,38) lies on it, so
38 = a(9)
a = 38/9
f(x) = (38/9)x^2 7 
f(x) = 4(x^26x)  9
= 4(x^26x+9) 4(9)  9
= 4(x3)^2 + 27
f(x) = a(x0)^2  7
38 = 9a7
a = 5
f(x) = 5x^2  7 
don't know where my  7 went ????

Thank You Guys!!!

F(x) = 4x^2+24x9.
h = B/2A = 24/8 = 3.
k = 4*3^2 + 24*3  9=36 + 72  9 = 27.
F(x) = a(xh)^2 + k.
F(x) = 4(x3)^2 + 27.