To determine the factors of the quadratic function given its zeros, let's go through the concept step-by-step.
1. Understanding Zeros of a Quadratic Function:
- A quadratic function \( f(x) \) can be expressed in the factored form as \( f(x) = a(x - \text{zero1})(x - \text{zero2}) \), where \( \text{zero1} \) and \( \text{zero2} \) are the zeros (or roots) of the function.
2. Given Zeros:
- In the problem, the zeros of the quadratic function are \( 3 \) and \( 8 \).
3. Formulating the Factors:
- Using the zeros \( \text{zero1} = 3 \) and \( \text{zero2} = 8 \), we form the factors by inserting these values into the expressions \( (x - \text{zero1}) \) and \( (x - \text{zero2}) \).
- Therefore, the factors of the quadratic function are:
[tex]\[
(x - 3) \quad \text{and} \quad (x - 8)
\][/tex]
4. Verifying the Options:
- Now, we match these factors with the given answer choices.
- A. \( (x + 8) \ \text{and} \ (x - 3) \)
- B. \( (x - 8) \ \text{and} \ (x + 3) \)
- C. \( (x + 8) \ \text{and} \ (x + 3) \)
- D. \( (x - 8) \ \text{and} \ (x - 3) \)
5. Correct Answer:
- From our formulation, the correct factors \((x - 3)\) and \((x - 8)\) correspond to option D: \((x - 8)\) and \((x - 3)\).
Hence, the correct answer is:
[tex]\[ \boxed{D. (x-8) \ \text{and} \ (x-3)} \][/tex]
