I NEED HELP ASAP

Question

Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=5x^2

but with the given maximum or minimum.

Maximum=1

at x=6

Answer 1

f(x) = 5x^2 has a minimum at the origin (0,0) which is the vertex

g(x) = 5(x-6)^2 + 1 has a minimum at (6,1) which is the vertex

in general h(x) = a(x-h)^2 + k where (h,k) is the vertex which is a minimum if a>0, and a max if a<0

IF you want the same shaped parabola with a maximum of 1 then

j(x) = -5(x-6)^2 + 1 is the same parabola flipped upside down and shifted to the new vertex of (6,1) which

is a maximum