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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.

Write a quadratic function f whose zeros are 11 and -2.

Learn how to write a quadratic function given zeros 11 and -2. This problem involves core algebraic concepts such as quadratic functions and factoring. Explore detailed steps, including expanding the expression and finding the final equation.

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