Answer:
y=-3(x-1)^2+5
Explanation:
The vertex form of a parabola is y=a(x-h)^2+k where (h,k) is the vertex.
We are given the vertex (h,k) is (1,5) so that makes the equation we have
y=a(x-1)^2+5.
We still need to find a.
We do have the point (0,2) on our parabola.
So replace (x,y) with (0,2) and solve for a.
2=a(0-1)^2+5
2=a(-1)^2+5
2=a(1)+5
2=a+5
-3=a
So the equation is
y=-3(x-1)^2+5