f\left(11\right)=\frac{1}{4}\left(5-x\right)^{2}

To find the value of \( f(11) \), we need to substitute \( x = 11 \) into the given function:

\[
f(x) = \frac{1}{4}\left(5 - x\right)^2
\]

Substitute \( x = 11 \):

\[
f(11) = \frac{1}{4}\left(5 - 11\right)^2
\]

Simplify inside the parentheses:

\[
f(11) = \frac{1}{4}\left(-6\right)^2
\]

Now, square \(-6\):

\[
f(11) = \frac{1}{4} \times 36
\]

Finally, multiply:

\[
f(11) = \frac{36}{4} = 9
\]

So, \( f(11) = 9 \).

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How would you find \( f(7) \) for the same function?
2. What is the vertex form of a quadratic function, and how does it relate to this problem?
3. How can you determine if the function \( f(x) = \frac{1}{4}(5-x)^2 \) opens upwards or downwards?
4. What is the range of the function \( f(x) = \frac{1}{4}(5-x)^2 \)?
5. How does the graph of \( f(x) = \frac{1}{4}(5-x)^2 \) compare to the graph of \( f(x) = x^2 \)?

**Tip:** When dealing with quadratic functions, always check if you can simplify the expression inside the square before performing further calculations.

Discover how to evaluate f(11) for the quadratic function f(x) = (1/4)(5 - x)^2. Follow a detailed step-by-step solution, including simplifying the expression, squaring negative numbers, and calculating the final result. Ideal for high school students studying quadratic functions and function evaluation.

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