find the parabola that passes through (0,0) with a vertex (2,4)

Question

I need the work / Steps  

Answer 1

Vertex form:  y=a(x-h)²+k

If (h,k)=(2,4)  then  y=a(x-2)²+4 now to get 'a' plug in (0,0)  so

0=a(0-2)² +4 -->  -4=a(-2)² --> 4a=-4 so a=-1 and y=-(x-2)²+4