Given f, of, x, equals, minus, 2, x, squared, plus, 2, xf(x)=−2x
2
+2x, find f, of, minus, 8f(−8)

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.

Learn how to evaluate the quadratic function f(x) = -2x^2 + 2x at x = -8 with a detailed step-by-step solution. This problem involves substituting the value into the function and simplifying the expression. Suitable for high school students.

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