Let’s solve the problem step by step.

Step 1: Understand the functions

1. Given:

   • $f(x) = 3(x^2 + 2)$
   • A table of values is provided for $h(x)$.

2. To determine the y-intercepts, substitute $x = 0$ into both functions.

Step 2: Calculate the y-intercept of $f(x)$

For $f(x) = 3(x^2 + 2)$: $f(0) = 3((0)^2 + 2) = 3(2) = 6.$ The y-intercept of $f(x)$ is 6.

Step 3: Determine the y-intercept of $h(x)$ from the table

From the table, when $x = 0$, $h(0) = -6$.
The y-intercept of $h(x)$ is -6.

Step 4: Compare the y-intercepts

The difference between the y-intercepts is: $f(0) - h(0) = 6 - (-6) = 6 + 6 = 12.$ Thus, the y-intercept of $f(x)$ is 12 units above the y-intercept of $h(x)$.

Step 5: Choose the correct answer

The correct statement is:
D. The y-intercept of $f(x)$ is 12 units above the y-intercept of $h(x)$.

Would you like further details or explanations?

5 Related Questions:

1. How do you find the y-intercept of a quadratic function?
2. What does the y-intercept represent graphically?
3. How do transformations affect the y-intercept of a function?
4. What are the steps to compare intercepts of two different functions?
5. How would the result change if $f(x)$ had a different constant term?

Tip:

Always substitute $x = 0$ to find the y-intercept of any function—this is where the graph crosses the y-axis.