To find \( f(8) \) for the function \( f(x) = 2x^2 - x - 12 \), substitute \( x = 8 \) into the equation:

\[
f(8) = 2(8^2) - (8) - 12
\]

Calculate \( 8^2 \):

\[
8^2 = 64
\]

Now substitute:

\[
f(8) = 2(64) - 8 - 12
\]

Calculate \( 2(64) \):

\[
2(64) = 128
\]

Now combine all the terms:

\[
f(8) = 128 - 8 - 12
\]
\[
f(8) = 128 - 20
\]
\[
f(8) = 108
\]

Thus, \( f(8) = 108 \).

Would you like any further details or have any questions? Here are some related questions you might consider:

1. How do you find the vertex of the quadratic function \( f(x) \)?
2. What are the roots of the equation \( 2x^2 - x - 12 = 0 \)?
3. How does the value of \( f(x) \) change as \( x \) increases?
4. What is the axis of symmetry for the function \( f(x) \)?
5. How would you graph the function \( f(x) = 2x^2 - x - 12 \)?

**Tip:** To quickly evaluate quadratic functions, use the vertex form or complete the square for insights on their maximum or minimum values.

Discover how to calculate f(8) for the quadratic function f(x) = 2x^2 - x - 12. This detailed solution involves substituting x = 8 and simplifying to find that f(8) equals 108. Ideal for students in Grades 7-9.

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