Question

Determine the equation of a parabola with vertex (1,5) and passes through point (0,2).

Answer 1

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