Question

write an equation of the parabola that has the same shape as the graph of f(x)=4x²,but with the point (-6,-2) as the vertex.

Answer 1

The graph must have the same shape as

$f(x)=4x^2$

but with the vertex at (-6,-2).

In general, the equation of the parabola in vertex form is

$y=a(x-h)^2+k$

where (h,k)=(-6,-2) in our case. By comparing both equations, we can see that the searched equation must be

$y=4(x+6)^2-2$