Question

Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=5x^2or g(x)=-5x^2, but with a given maximum of minimum
Maximum=2 at x=-4

Answer 1

F(x)=5x^2 Has minimum (0,0)

g(x) = f(x) + 2 Shifts the graph two units up, then the minimum is 2+0=2.

h(x) = g(x+4) Shifts the graph four units left,  then the minimum is at 0-4 = -4.

Then h(x) = 5(x+4)^2 + 2 has the minimum (-4,2)

And p(x) = -5(x+4)^2 + 2 has the maximum (-4,2)