Question

The table describes the quadratic function h(x).

x h(x)
−3 1
−2 −2
−1 −3
0 −2
1 1
2 6
3 13


What is the equation of h(x) in vertex form?



a
h(x) = (x − 1)2 + 1

b
h(x) = (x − 1)2 + 3

c
h(x) = (x + 1)2 − 1

d
h(x) = (x + 1)2 − 3

Answer 1

I think the answer is b

Answer 2

Answer: The answer is (A) h(x) = (x - 1)^2 + 1.

Step-by-step explanation: We can use the vertex form of a quadratic function, which is given by:

h(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola. To find this vertex, we can use the formula:

h = -b/2a

where a and b are coefficients of the quadratic function in standard form (ax^2 + bx + c). Once we find h, we can substitute it in the vertex form to find the value of k.

From the given table, we can see that the vertex of the parabola is at (1, 1) (since h(x) has its maximum value at x=3 and its minimum value at x=-1, which means the vertex is at x=1). Therefore, we have:

h = 1

k = h(1) = 1

Substituting these values in the vertex form, we get:

h(x) = a(x - 1)^2 + 1

To find the value of a, we can use any point from the table. Let's use the point (-2, -2):

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

-2 = 9a + 1

9a = -3

a = -1/3

Therefore, the equation of h(x) in vertex form is:

h(x) = (-1/3)(x - 1)^2 + 1

So the answer is (a) h(x) = (x - 1)^2 + 1.