https://file.aiquickdraw.com/mathbot/file/1726283728106mz09cguv.jpg

From the graph and the equation \(y = 3x - x^2\), let's determine the intercepts.

### Finding the x-intercepts:
The x-intercepts occur where \(y = 0\). Setting the equation to zero:
\[ 0 = 3x - x^2 \]
\[ x^2 - 3x = 0 \]
Factoring out \(x\):
\[ x(x - 3) = 0 \]
Setting each factor equal to zero:
\[ x = 0 \quad \text{and} \quad x = 3 \]

### Finding the y-intercept:
The y-intercept occurs where \(x = 0\). Substituting into the equation:
\[ y = 3(0) - 0^2 = 0 \]

### Solutions:
- x-intercept (smaller x-value): \((0, 0)\)
- x-intercept (larger x-value): \((3, 0)\)
- y-intercept: \((0, 0)\)

These answers are consistent with the graph provided. If you have any questions or need further details, feel free to ask.

### Related Questions:
1. How do you determine the vertex of the parabola \(y = 3x - x^2\)?
2. What is the axis of symmetry for the equation \(y = 3x - x^2\)?
3. How can you verify the intercepts algebraically without a graph?
4. What transformations have been applied if the original equation was \(y = -x^2\)?
5. How would the graph change if the equation was \(y = x^2 - 3x\)?

### Tip:
When you have a quadratic equation in the form \(y = ax^2 + bx + c\), setting \(y = 0\) and factoring can directly give you the x-intercepts.

Find the x- and y-intercepts from the graph of the equation y = 3x - x^2.

Learn how to find the x-intercepts and y-intercepts of the quadratic equation y = 3x - x^2. This step-by-step solution explains how to factor the quadratic equation and check the intercepts on the graph. Suitable for students in Grades 8-10.

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