Question

The table describes the quadratic function p(x).

x p(x)
−1 31
0 17
1 7
2 1
3 −1
4 1
5 7

What is the equation of p(x) in vertex form?
p(x) = 2(x − 3)2 − 1
p(x) = 2(x + 3)2 − 1
p(x) = 3(x − 3)2 − 1
p(x) = 3(x + 3)2 − 1

Answer 1

`p(x)=2(x-3)^2-1`

Explanation:

The values are symmetric about
`x=3`, meaning the equation is of the form
`p(x)=a(x-3)^2-1`.

Since
`p(4)=1`, it follows that:

`1=a-1 \\ \\ a=2`

Therefore,
`p(x)=2(x-3)^2-1`.