Given f, of, x, equals, minus, 3, x, squared, plus, 6, x, plus, 1f(x)=−3x 
2
 +6x+1, find f, of, 6f(6)

To find \( f(6) \) given that \( f(x) = -3x^2 + 6x + 1 \), we substitute \( x = 6 \) into the equation for \( f(x) \).

\[
f(6) = -3(6)^2 + 6(6) + 1
\]

Now calculate each term:

\[
f(6) = -3(36) + 36 + 1
\]

\[
f(6) = -108 + 36 + 1
\]

\[
f(6) = -108 + 37
\]

\[
f(6) = -71
\]

So, \( f(6) = -71 \).

Would you like a detailed breakdown of any step, or have any questions?

Here are 5 related questions:
1. What is \( f(0) \) for the same function?
2. Find the vertex of the parabola \( f(x) = -3x^2 + 6x + 1 \).
3. What are the roots of \( f(x) = 0 \)?
4. How does the sign of the leading coefficient affect the graph of the quadratic function?
5. Find \( f'(x) \) and evaluate \( f'(6) \).

**Tip:** The sign of the leading coefficient in a quadratic function affects whether the parabola opens upwards or downwards!

Learn how to solve for f(6) in the quadratic function f(x) = -3x^2 + 6x + 1. This solution involves substituting x = 6 into the equation and evaluating it step-by-step. Ideal for students in Grades 9-11 learning algebra and quadratic functions.

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