https://file.aiquickdraw.com/mathbot/file/1726873845432u17oyenw.jpg

The problem is asking to evaluate the function \( g(x) = -x^2 + 6x + 1 \) at \( x = -3 \).

### Step-by-Step Solution:

1. **Start with the given function:**
   \[
   g(x) = -x^2 + 6x + 1
   \]

2. **Substitute \( x = -3 \) into the equation:**
   \[
   g(-3) = -(-3)^2 + 6(-3) + 1
   \]

3. **Simplify each term:**
   - \( (-3)^2 = 9 \), so the first term becomes \( -9 \)
   - The second term is \( 6(-3) = -18 \)
   - The third term remains as \( +1 \)

   Therefore, the expression becomes:
   \[
   g(-3) = -9 - 18 + 1
   \]

4. **Add the terms:**
   \[
   g(-3) = -9 - 18 + 1 = -26
   \]

### Final Answer:
\[
g(-3) = -26
\]

Would you like further clarification on this solution? Here are 5 related questions you could explore:

1. How does substituting different values into the function affect the result?
2. What are the key characteristics of a quadratic function like \( g(x) = -x^2 + 6x + 1 \)?
3. How would you graph the function \( g(x) = -x^2 + 6x + 1 \)?
4. How do you find the vertex of the quadratic function \( g(x) \)?
5. What does the negative sign in front of \( x^2 \) signify in terms of the graph's shape?

**Tip:** When working with quadratic functions, always simplify carefully after substituting values to avoid mistakes!

Let g(x) = -x^2 + 6x + 1. Find and simplify g(-3).

Learn how to evaluate the quadratic function g(x) = -x^2 + 6x + 1 at x = -3 with a detailed step-by-step solution. This problem covers key algebraic concepts such as substitution and simplification, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation