To solve the problem $f(x) = -2x^2 + 2x$ and find $f(-8)$, follow these steps:

Step 1: Substitute $x = -8$ into the function $f(x)$.

$f(-8) = -2(-8)^2 + 2(-8)$

Step 2: Simplify the expression.

• First, calculate $(-8)^2$:

  $(-8)^2 = 64$

• Now, substitute $64$ into the expression:

  $f(-8) = -2(64) + 2(-8)$

• Multiply:

  $f(-8) = -128 - 16$

• Finally, add the terms:

  $f(-8) = -144$

So, $f(-8) = -144$.

Would you like to explore the concepts involved further or ask additional questions?

Here are some related questions:

1. What is the vertex of the parabola described by $f(x) = -2x^2 + 2x$?
2. How do you find the roots of $f(x) = -2x^2 + 2x$?
3. What does the graph of $f(x) = -2x^2 + 2x$ look like?
4. How does the function $f(x) = -2x^2 + 2x$ change as $x$ increases?
5. Can you find the value of $f(x)$ when $x = 1$?

Tip: When dealing with quadratic functions, remember that the sign of the coefficient of $x^2$ determines whether the parabola opens upwards or downwards.