Given f(x)=13(2−x)2f(x)=13(2−x)2, what is the value of f(8)f(8)?

To find the value of \( f(8) \) for the function \( f(x) = 13(2 - x)^2 \), we substitute \( x = 8 \) into the function:

\[
f(8) = 13(2 - 8)^2
\]

Calculating \( 2 - 8 \):

\[
2 - 8 = -6
\]

Now, square \( -6 \):

\[
(-6)^2 = 36
\]

Then, multiply by 13:

\[
f(8) = 13 \times 36 = 468
\]

Thus, the value of \( f(8) \) is \( 468 \).

If you have any questions or need further details, feel free to ask! Here are some related questions:

1. What is the general form of \( f(x) \)?
2. How does changing \( x \) affect the value of \( f(x) \)?
3. What is the value of \( f(0) \)?
4. Can you find the vertex of the parabola represented by \( f(x) \)?
5. How would the function change if the coefficient before \( (2 - x)^2 \) were different? 

**Tip:** Always check the behavior of functions at critical points to understand their shape!

Given f(x)=13(2−x)², what is the value of f(8)?

Discover how to calculate f(8) for the function f(x) = 13(2 - x)². This step-by-step solution demonstrates the substitution process and provides insight into the behavior of quadratic functions. Ideal for Grades 6-8.

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