https://file.aiquickdraw.com/mathbot/file/1726232908175g58blej8.jpg

Here's the graph of the function \( f(x) = -x^2 + 3 \), with values plotted for \( x \) ranging from -3 to 3. The red points represent key values of the function.

### Summary of the Graph:
- **Vertex**: \( (0, 3) \), the highest point.
- **Axis of Symmetry**: The line \( x = 0 \) (the y-axis).
- **X-intercepts**: \( x \approx \pm \sqrt{3} \approx \pm 1.732 \).
- **Y-intercept**: \( (0, 3) \).

### Table of Values:
| \( x \)   | \( f(x) \) |
|:--------:|:----------:|
|  -3      |    -6      |
|  -2      |    -1      |
|  -1      |    2       |
|   0      |    3       |
|   1      |    2       |
|   2      |    -1      |
|   3      |    -6      |

Would you like more details or explanations?

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Here are five related questions to explore:
1. How would the graph change if the function were \( f(x) = x^2 + 3 \)?
2. How can we find the vertex of a parabola using a different method, such as completing the square?
3. How do the x-intercepts change when we adjust the constant in the function?
4. What happens to the graph if the coefficient of \( x^2 \) becomes more negative, like \( -2x^2 + 3 \)?
5. How do we determine the domain and range of a quadratic function?

**Tip:** For quadratic functions like this one, the sign of the \( x^2 \)-term always determines whether the parabola opens upwards (positive) or downwards (negative).

Graph and fully describe the function f(x) = -x^2 + 3. Graph values of x from -3 to 3.

Explore how to graph and describe the quadratic function f(x) = -x^2 + 3 for values of x from -3 to 3. This problem focuses on identifying key features like the vertex, axis of symmetry, and intercepts.

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