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To write a quadratic function \( f(x) \) with given zeros of \( -6 \) and \( -2 \), we use the fact that a quadratic function can be written in factored form as:

\[
f(x) = a(x - r_1)(x - r_2)
\]

where \( r_1 \) and \( r_2 \) are the zeros of the function.

In this case, the zeros are \( -6 \) and \( -2 \), so the factored form of the quadratic function will be:

\[
f(x) = a(x + 6)(x + 2)
\]

To simplify, expand the expression:

\[
f(x) = a[(x + 6)(x + 2)] = a(x^2 + 2x + 6x + 12) = a(x^2 + 8x + 12)
\]

If there are no further conditions (such as a specific value for \( a \)), we can assume \( a = 1 \), giving us:

\[
f(x) = x^2 + 8x + 12
\]

This is the quadratic function with zeros at \( -6 \) and \( -2 \).

Would you like more details on any part of this process, or have any further questions?

Here are 5 related questions:
1. How do you find the zeros of a quadratic function?
2. What role does the constant \( a \) play in a quadratic function?
3. How can you verify that \( f(x) = x^2 + 8x + 12 \) has zeros at \( -6 \) and \( -2 \)?
4. How do you convert a quadratic function from factored form to standard form?
5. Can a quadratic function have complex zeros, and how does that affect the function?

**Tip:** When expanding factored forms, distribute each term carefully to avoid mistakes.

Write a quadratic function f whose zeros are -6 and -2.

Learn how to write a quadratic function with given zeros of -6 and -2. This solution includes the factored form and expanded standard form, with step-by-step explanations. Ideal for students in Grades 8-10.

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