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The image shows the following problem:

"Given the function \( f(x) = \frac{1}{4}x^2 - 1 \), find the value of \( f\left( \frac{-1}{2} \right) \) in simplest form."

Let's solve this step-by-step:

### Step 1: Write the function
The function is given as:
\[
f(x) = \frac{1}{4}x^2 - 1
\]

### Step 2: Substitute \( x = \frac{-1}{2} \) into the function
We are asked to find \( f\left( \frac{-1}{2} \right) \), so we substitute \( x = \frac{-1}{2} \) into the equation:
\[
f\left( \frac{-1}{2} \right) = \frac{1}{4}\left( \frac{-1}{2} \right)^2 - 1
\]

### Step 3: Simplify the expression
Now, simplify the square of \( \frac{-1}{2} \):
\[
\left( \frac{-1}{2} \right)^2 = \frac{1}{4}
\]
So the expression becomes:
\[
f\left( \frac{-1}{2} \right) = \frac{1}{4} \times \frac{1}{4} - 1
\]
\[
f\left( \frac{-1}{2} \right) = \frac{1}{16} - 1
\]

### Step 4: Simplify further
To subtract, express 1 as \( \frac{16}{16} \):
\[
f\left( \frac{-1}{2} \right) = \frac{1}{16} - \frac{16}{16}
\]
\[
f\left( \frac{-1}{2} \right) = \frac{1 - 16}{16}
\]
\[
f\left( \frac{-1}{2} \right) = \frac{-15}{16}
\]

### Final Answer:
The value of \( f\left( \frac{-1}{2} \right) \) is \( \frac{-15}{16} \).

Do you have any questions or would you like more details?

### Related Questions:
1. How would the answer change if \( f(x) = \frac{1}{2}x^2 - 1 \)?
2. Can you explain how squaring a fraction works in more detail?
3. What happens if \( x = 0 \) in the function \( f(x) \)?
4. How do we handle negative exponents in functions like this?
5. How do we simplify fractions with different denominators?

### Tip:
Always double-check your steps when squaring fractions or simplifying negative numbers to avoid small errors.

Given the function f(x) = (1/4)x^2 - 1, find the value of f(-1/2) in simplest form.

Learn how to evaluate the function f(x) = (1/4)x^2 - 1 by substituting x = -1/2. Follow a detailed step-by-step solution, including substitution and simplification of fractions. Suitable for students in Grades 7-9.

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