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The given equation is \( y = 3x - x^2 \), and the graph is a downward-facing parabola. Based on the graph, we need to identify the intercepts.

### Steps:

1. **Y-Intercept:**
   The y-intercept occurs where \( x = 0 \). Substituting \( x = 0 \) into the equation:
   \[
   y = 3(0) - (0)^2 = 0
   \]
   So, the y-intercept is \( (0, 0) \).

2. **X-Intercepts:**
   The x-intercepts occur where \( y = 0 \). Setting \( y = 0 \) in the equation:
   \[
   0 = 3x - x^2
   \]
   Rearranging this gives:
   \[
   x^2 - 3x = 0
   \]
   Factoring the equation:
   \[
   x(x - 3) = 0
   \]
   So, \( x = 0 \) or \( x = 3 \).
   Therefore, the x-intercepts are at \( (0, 0) \) and \( (3, 0) \).

### Summary of intercepts:
- **Smaller x-intercept:** \( (0, 0) \)
- **Larger x-intercept:** \( (3, 0) \)
- **Y-intercept:** \( (0, 0) \)

Would you like more details on any of the steps?

Here are 5 related questions for further practice:
1. How do you find the vertex of the parabola \( y = 3x - x^2 \)?
2. What is the axis of symmetry for the given parabola?
3. How would you determine the direction of the parabola (upward or downward)?
4. Can you calculate the maximum or minimum value of the parabola?
5. How do you solve for intercepts algebraically in general quadratic equations?

**Tip:** For quadratic equations, always check if factoring is possible before using the quadratic formula. It simplifies your calculations!

Find the x- and y-intercepts for the equation y = 3x - x^2 based on the graph.

This page explains how to find the x- and y-intercepts for the quadratic equation y = 3x - x^2. It covers algebraic concepts like solving quadratic equations by factoring and analyzing the graph of the parabola. Suitable for students in Grades 9-10.

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