The equation \( y = 9 - x^2 \) represents a parabola in the coordinate plane. 

### Key features of the parabola:
1. **Vertex**: The vertex of the parabola is the highest point on the graph since the coefficient of \( x^2 \) is negative. For the equation \( y = 9 - x^2 \), the vertex is at \( (0, 9) \).
2. **Axis of Symmetry**: The axis of symmetry is the vertical line that passes through the vertex. For this parabola, the axis of symmetry is \( x = 0 \).
3. **Direction**: The parabola opens downwards because the coefficient of \( x^2 \) is negative.
4. **Intercepts**:
   - **Y-intercept**: The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation gives \( y = 9 \). So, the y-intercept is \( (0, 9) \).
   - **X-intercepts**: The x-intercepts occur when \( y = 0 \). Setting \( y = 0 \) in the equation and solving for \( x \) gives:
     \[
     0 = 9 - x^2 \implies x^2 = 9 \implies x = \pm 3
     \]
     So, the x-intercepts are \( (-3, 0) \) and \( (3, 0) \).

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Here are five related questions to expand on this topic:
1. How do you find the focus and directrix of the parabola \( y = 9 - x^2 \)?
2. What is the standard form of a parabola and how does it compare to \( y = 9 - x^2 \)?
3. How would you graph the equation \( y = 9 - x^2 \)?
4. Can you derive the vertex form of the equation from \( y = 9 - x^2 \)?
5. How does changing the coefficient of \( x^2 \) affect the shape of the parabola?

**Tip:** When analyzing a quadratic equation, always check the coefficient of \( x^2 \) to determine if the parabola opens upwards or downwards.

Explore the equation y = 9 - x^2, a quadratic equation that forms a parabola with specific features such as vertex, axis of symmetry, and intercepts. Learn how to graph this parabola and understand the impact of changing the coefficient of x^2. Suitable for Grades 9-12 students.

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