Question

The table describes the quadratic function p(x).

x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46

What is the equation of p(x) in vertex form?
a. p(x) = 2(x − 1)2 − 2
b. p(x) = 2(x + 1)2 − 2
c. p(x) = 3(x − 1)2 − 2
d. p(x) = 3(x + 1)2 − 2

Answer 1

Answer: the equation of p(x) in vertex form is:

p(x) = (x - 2)^2 + 1

Explanation:

To find the equation of the quadratic function in vertex form, we need to determine the values of a, h, and k in the equation p(x) = a(x - h)^2 + k.

From the given table, we can observe that the vertex of the quadratic function is at the point (2, 1) because the value of p(x) is the lowest at x = 2. Therefore, the value of h is 2.

To find the value of k, we can substitute the vertex coordinates (2, 1) into the equation. So we have:

1 = a(2 - 2)^2 + k

1 = a(0) + k

1 = k

Now we have the values of h = 2 and k = 1. We need to find the value of a. To do that, we can substitute one of the other points from the table into the equation.

Let's use the point (-1, 10):

10 = a(-1 - 2)^2 + 1

10 = a(-3)^2 + 1

10 = 9a + 1

9a = 10 - 1

9a = 9

a = 1

Now we have the values of a = 1, h = 2, and k = 1. Plugging these values into the vertex form equation, we get:

p(x) = 1(x - 2)^2 + 1

Simplifying this equation, we find:

p(x) = (x - 2)^2 + 1