Given f, of, x, equals, minus, x, squared, plus, 2, x, plus, 9*f*(*x*)=−*x*2+2*x*+9, find f, of, 3*f*(3)

To find \( f(3) \) given the function \( f(x) = -x^2 + 2x + 9 \), we simply substitute \( x = 3 \) into the function.

\[
f(3) = -(3)^2 + 2(3) + 9
\]

Let's calculate this step by step:

1. \( (3)^2 = 9 \)
2. \( -9 = -9 \) (from the \( -(3)^2 \) term)
3. \( 2(3) = 6 \)
4. Now, substitute into the function:

\[
f(3) = -9 + 6 + 9
\]

5. Simplify the expression:

\[
f(3) = (-9 + 6) + 9 = -3 + 9 = 6
\]

So, \( f(3) = 6 \).

Would you like more details or have any questions about this solution?

---

Here are five related questions for practice:

1. What is \( f(0) \) for the same function \( f(x) = -x^2 + 2x + 9 \)?
2. Find the vertex of the parabola described by \( f(x) = -x^2 + 2x + 9 \).
3. For which value of \( x \) does \( f(x) = 0 \)?
4. Calculate \( f(-2) \) using the same function.
5. Determine the axis of symmetry for the function \( f(x) = -x^2 + 2x + 9 \).

**Tip:** When evaluating a function at a specific point, always substitute the value directly and simplify carefully step by step to avoid errors.

Learn how to evaluate f(3) for the function f(x) = -x^2 + 2x + 9. Step-by-step solution provided with detailed calculations. Explore related practice questions on function evaluation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation