https://file.aiquickdraw.com/mathbot/file/1726883206749q5ubppu5.jpg

To solve the problem in the image, we need to find \( f\left(\frac{1}{2}\right) \) for the given function \( f(x) = 3x^2 - 7x - 7 \).

### Steps to solve:

1. Substitute \( x = \frac{1}{2} \) into the function \( f(x) = 3x^2 - 7x - 7 \).
   
   \[
   f\left( \frac{1}{2} \right) = 3\left( \frac{1}{2} \right)^2 - 7\left( \frac{1}{2} \right) - 7
   \]

2. Simplify each term:

   - \( 3\left( \frac{1}{2} \right)^2 = 3 \times \frac{1}{4} = \frac{3}{4} \)
   - \( 7 \times \frac{1}{2} = \frac{7}{2} \)

3. Now, substitute these values back into the equation:

   \[
   f\left( \frac{1}{2} \right) = \frac{3}{4} - \frac{7}{2} - 7
   \]

4. Convert all terms to have a common denominator (denominator of 4):

   \[
   \frac{7}{2} = \frac{14}{4}, \quad 7 = \frac{28}{4}
   \]

   So the expression becomes:

   \[
   f\left( \frac{1}{2} \right) = \frac{3}{4} - \frac{14}{4} - \frac{28}{4}
   \]

5. Combine the terms:

   \[
   f\left( \frac{1}{2} \right) = \frac{3 - 14 - 28}{4} = \frac{-39}{4}
   \]

### Conclusion:

The value of \( f\left( \frac{1}{2} \right) \) is \( \frac{-39}{4} \), so the correct answer is option **D**.

Would you like further details or have any questions about the steps? Here are some related questions to expand your understanding:

1. How do you find the value of a function at a given point?
2. What are common denominators, and how do you find them when combining fractions?
3. How do quadratic functions behave, and what is their general shape?
4. What is the importance of simplifying terms in algebraic expressions?
5. How can you verify the solution to a quadratic function?

**Tip:** Always double-check each step when substituting values, especially when dealing with fractions.

Find the value of f(1/2) for the quadratic function f(x) = 3x^2 - 7x - 7. This problem involves substitution and simplification with fractions, a key skill in algebra for Grades 8-10.

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