Question

The table describes the quadratic function h(x).

x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22

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

Answer 1

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To find the equation of the quadratic function h(x) in vertex form, we need to determine the vertex of the parabola. The vertex form of a quadratic function is h(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Looking at the table of values, we can see that the vertex must be one of the points in the middle because the function changes direction from decreasing to increasing. The points (0, 1) and (1, 6) are where this change occurs. Let's calculate the vertex using one of these points:

Vertex (h, k) = (0, 1)

Now we can plug these values into the vertex form:

h(x) = a(x - 0)^2 + 1

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

Next, we need to find the value of 'a'. We can use any of the given points from the table. Let's use (2, 13):

13 = a(2^2) + 1

13 = 4a + 1

Now, solve for 'a':

4a = 13 - 1

4a = 12

a = 3

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

h(x) = 3x^2 + 1