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:

Would you like more details or explanations?

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).