Question: What is the sum, $h(x)$, of the functions $f(x) = 4x^2 - 2x + 6$ and $g(x) = 2x^2 + x - 5$?
1. **State the problem:** We need to find the sum $h(x)$ of two functions $f(x)$ and $g(x)$ where:
$$f(x) = 4x^2 - 2x + 6$$
$$g(x) = 2x^2 + x - 5$$
2. **Formula for sum of functions:** The sum $h(x)$ is given by:
$$h(x) = f(x) + g(x)$$
3. **Add the functions term-by-term:**
$$h(x) = (4x^2 - 2x + 6) + (2x^2 + x - 5)$$
Group like terms:
$$h(x) = (4x^2 + 2x^2) + (-2x + x) + (6 - 5)$$
4. **Simplify each group:**
$$h(x) = 6x^2 - x + 1$$
5. **Final answer:**
The sum of the functions is:
$$h(x) = 6x^2 - x + 1$$
This corresponds to option D.