It seems you want to evaluate the function \( f(x) = -3x^2 + 6x + 1 \) at \( x = 6 \).

Let's calculate \( f(6) \):

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

First, calculate \( 6^2 \):

\[
6^2 = 36
\]

Now multiply by \(-3\):

\[
-3 \times 36 = -108
\]

Next, calculate \( 6 \times 6 \):

\[
6 \times 6 = 36
\]

Now, add these results together along with the constant term \( 1 \):

\[
f(6) = -108 + 36 + 1 = -71
\]

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

Would you like more details on this calculation, or do you have any other questions?

Here are 5 related questions to consider:

1. How would you find the roots of the function \( f(x) = -3x^2 + 6x + 1 \)?
2. What is the vertex of the parabola represented by the function \( f(x) = -3x^2 + 6x + 1 \)?
3. How does changing the coefficient of \( x^2 \) in the function \( f(x) \) affect the shape of the parabola?
4. Can you determine the axis of symmetry for the function \( f(x) = -3x^2 + 6x + 1 \)?
5. What is the y-intercept of the function \( f(x) = -3x^2 + 6x + 1 \)?

**Tip:** When evaluating a function, always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Learn how to evaluate the function f(x) = -3x^2 + 6x + 1 at x = 6 with a step-by-step solution. This problem involves quadratic equations, function evaluation, and follows the order of operations (PEMDAS). Suitable for high school students.

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