Question

If the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola, find an equation for the parabola. Write your answer in the form () = ( − ℎ)2 + .

Answer 1

`y=-1(x-2)^2+3`

Explanation:

W have been given that the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola. We are asked to find the equation of parabola in the form
`y=(x-h)^2+k`.

We know that vertex form of parabola in form
`y=a(x-h)^2+k`, where (h,k) in vertex of parabola.

Upon substituting coordinates of vertex, we will get:

`y=a(x-2)^2+3`

To find the value of a, we will substitute coordinates of point (0, -1) as:

`-1=a(0-2)^2+3`

`-1=a(4)+3`

`-1=4a+3`

`-1-3=4a+3-3`

`-4=4a`

`(-4)/(4)=(4a)/(4)`

`-1=a`

Therefore, our required equation would be
`y=-1(x-2)^2+3`.