Find Vertex form of a graph

Question

I need to find the vertex form of the graph. But I can't figure out how to find a, in f(x)=a(x-h)^2+k. Is it possible that you could help explain this to me.

Answer 1

the vertex is the point (h,k) in the equation y = f(x) = a(x-h)^2 + k

"a" tells you how flat or vertical the parabola is

you have one point on the parabola (h,k), now find a 2nd point, anywhere on the parabola and plug it in, call it (c,d)

then plug it in and solve for "a"

d = a(c-h)^2 +k

a(c-h)^2 = d-k

a = (d-k)/(c-h)^2

the flatter the parabola, the smaller a is

if the parabola is upward opening, a >0

if the parabola opens downward a<0

the more vertical each half of the parabola the larger the absolute value of a