The function h(x) is a continuous quadratic function with a domain of all real numbers. The table lists some of the points on the function.
x | h(x)
--------------
-2 | 8
0 | 2
2 | -2
Using the points provided, we can see that the function is a downward-facing parabola. Let's write the equation of the function in the form of h(x) = ax^2 + bx + c, where a, b, and c are constants.
Let's start by substituting the point (0, 2) into the equation:
h(0) = a(0)^2 + b(0) + c
2 = c
Now, let's substitute the points (-2, 8) and (2, -2) into the equation:
h(-2) = a(-2)^2 + b(-2) + 2
8 = 4a - 2b + 2
h(2) = a(2)^2 + b(2) + 2
-2 = 4a + 2b + 2
Now we have a system of three equations:
1) 2 = c
2) 8 = 4a - 2b + 2
3) -2 = 4a + 2b + 2
From equation 1, we know that c = 2. Substitute c = 2 into equations 2 and 3:
8 = 4a - 2b + 2
-2 = 4a + 2b + 2
Simplify the equations:
4 = 4a - 2b
-4 = 4a + 2b
Add the equations:
0 = 8a
a = 0
Now, substitute a = 0 back into one of the equations:
4 = -2b
b = -2
Therefore, the equation of the function h(x) is h(x) = -2x + 2.