To write a quadratic function $h(x)$ whose zeros (or roots) are 11 and -3, we can use the fact that a quadratic function can be written in factored form as:

$h(x) = a(x - r_1)(x - r_2)$

where $r_1$ and $r_2$ are the zeros (roots) of the quadratic function, and $a$ is a constant that can scale the function (often set to 1 for simplicity).

Given the zeros 11 and -3, we substitute these into the factored form:

$h(x) = a(x - 11)(x + 3)$

For simplicity, we can choose $a = 1$, which gives:

$h(x) = (x - 11)(x + 3)$

Now, expand the expression:

$h(x) = x^2 + 3x - 11x - 33$

$h(x) = x^2 - 8x - 33$

So, the quadratic function is:

$h(x) = x^2 - 8x - 33$

---

Would you like a more detailed explanation or further steps?

Here are some related questions to explore:

1. How do you find the zeros of a quadratic equation from its factored form?
2. What is the vertex of the quadratic function $h(x) = x^2 - 8x - 33$?
3. How can you write a quadratic equation given its vertex and one point on the graph?
4. What is the process of completing the square to find the roots of a quadratic function?
5. How does the value of $a$ affect the graph of the quadratic function?

Tip: To quickly find the vertex of a quadratic function, you can use the formula $x = \frac{-b}{2a}$ from the standard form $ax^2 + bx + c$.