The problem is asking to write a quadratic function $f(x)$ whose zeros are 11 and -2.

To construct a quadratic function from its zeros (roots), we use the fact that if a quadratic equation has roots $r_1$ and $r_2$, the corresponding quadratic function can be written as:

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

Here, the zeros are $r_1 = 11$ and $r_2 = -2$, so the function becomes:

$f(x) = a(x - 11)(x + 2)$

Now, we'll expand the expression:

$f(x) = a \left[(x - 11)(x + 2)\right]$ $f(x) = a(x^2 + 2x - 11x - 22)$ $f(x) = a(x^2 - 9x - 22)$

If no value for $a$ is given, we assume $a = 1$, so the quadratic function becomes:

$f(x) = x^2 - 9x - 22$

Thus, the quadratic function is:

$f(x) = x^2 - 9x - 22$

Would you like any additional details or clarifications on this?

Here are five related questions for further understanding:

1. How do you determine the equation of a quadratic function from given roots?
2. What is the significance of the coefficient $a$ in the general form of a quadratic equation?
3. Can a quadratic function have more than two zeros?
4. How do you factor a quadratic equation to find its roots?
5. What role does the discriminant play in determining the nature of the roots of a quadratic equation?

Tip: Always check the sign of the zeros when constructing a quadratic function to avoid errors.