HI! I don't understand how to get this answer, can someone please help me! Thanks

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

Vertex form is p(x) = a(x - h)² + k, where (h,k) is the vertex

The graph is a parabola symmetric about the vertical line that goes through the vertex.

From the given table, the values of p(x) are the same for x=2 and x =4, the values are the same for

x = 1 and x = 5, etc

The graph is symmetric about the vertical line x = 3. So the vertex is (3, -1)

Therefore, p(x) = a(x - 3)² - 1

Since (0,17) is on the graph, 17 = 9a - 1. So, a = 2

p(x) = 2(x - 3)² - 1

Answer 2

It is an upward opening parabola.

The vertex, lowest point, is at (3, -1)

p(x) = a(x - 3)² - 1

Substitute any other point to solve for a.