Given f, of, x, equals, minus, x, squared, plus, 6, xf(x)=−x 
2
 +6x, find f, of, minus, 4f(−4)


Given the function \( f(x) = -x^2 + 6x \), we want to find \( f(-4) \).

To do this, substitute \( x = -4 \) into the function \( f(x) \).

\[
f(-4) = -(-4)^2 + 6(-4)
\]

Step-by-step:

1. \( (-4)^2 = 16 \), so the expression becomes:
   \[
   f(-4) = -16 + 6(-4)
   \]

2. \( 6(-4) = -24 \), so the expression is now:
   \[
   f(-4) = -16 - 24
   \]

3. Simplifying:
   \[
   f(-4) = -40
   \]

Thus, \( f(-4) = -40 \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the vertex of the quadratic function \( f(x) = -x^2 + 6x \)?
2. How do you find the roots of \( f(x) = -x^2 + 6x \)?
3. How would you complete the square for \( f(x) = -x^2 + 6x \)?
4. What is the axis of symmetry for the graph of \( f(x) = -x^2 + 6x \)?
5. How does the function \( f(x) = -x^2 + 6x \) compare to \( g(x) = x^2 - 6x \)?

**Tip**: When dealing with quadratic functions, always remember that the vertex form can help you identify the maximum or minimum value of the function easily.

Learn how to evaluate the quadratic function f(x) = -x^2 + 6x at x = -4. This step-by-step solution involves key algebraic concepts like function substitution and quadratic function evaluation, making it ideal for students in Grades 8-10.

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