find the vertex form for the quadratic function that passes through (4,12) and has a minimum at (2,-4)

Question

find the vertex form for the quadratic function that passes through (4,12) and has a minimum at (2,-4)

Answer 1

A quadratic function is a parabola, when graphed. If it has a minimum, then it's opening upwardly and the vertex coordinates are (h,k) at the minimum value of the function. Thus (h,k) = (2,-4).

 

The general equation is y - k = a(x - h)² and you can substitute the coordinates (4,12) in for (x,y); then you will be able to determine the value of a.