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The equation you need to plot is \( y = 10 - x^2 \). This is a downward-opening parabola with the vertex at the point (0,10). The vertex represents the maximum value of \( y \) because the coefficient of \( x^2 \) is negative. Below is the step-by-step plotting for the given graph:

### Steps for Plotting \( y = 10 - x^2 \)

1. **Determine the Vertex**: The vertex of the parabola \( y = 10 - x^2 \) is at (0, 10).

2. **Calculate y-intercept**: When \( x = 0 \), \( y = 10 - 0^2 = 10 \). So, the y-intercept is at (0, 10).

3. **Find additional points**:
   - When \( x = 1 \) or \( x = -1 \), \( y = 10 - 1^2 = 9 \).
   - When \( x = 2 \) or \( x = -2 \), \( y = 10 - 4 = 6 \).
   - When \( x = 3 \) or \( x = -3 \), \( y = 10 - 9 = 1 \).

4. **Plot the Points**:
   - (0, 10), (1, 9), (-1, 9), (2, 6), (-2, 6), (3, 1), (-3, 1).

5. **Draw the Parabola**: Connect these points with a smooth curve to form the parabola. It should open downwards, with the vertex at (0, 10).

### Graphed Points
Here's the list of points you might mark on the graph for clarity:
- (0, 10)
- (±1, 9)
- (±2, 6)
- (±3, 1)

Now, go ahead and plot these points on the paper, then draw the smooth curve of the parabola connecting them. If you want more points for a smoother curve or any details, just let me know!

**Further Queries:**
1. Would you like to know why the parabola opens downward?
2. Do you need help with finding the x-intercepts?
3. Are you interested in understanding the effect of changing coefficients in the equation \( y = a - x^2 \)?
4. Would you like to see how the graph changes if the equation were \( y = x^2 - 10 \)?
5. Need to understand how the symmetry of the parabola about the y-axis helps in plotting?

**Tip:** Always check symmetry in parabolas to reduce the workload—plot points for positive x and mirror them for negative x.

Plot the graph of the equation y = 10 - x^2.

Learn how to plot the quadratic equation y = 10 - x^2 step by step. This lesson covers the calculation of the vertex, identifying key points, and drawing a downward-opening parabola. Ideal for students in Grades 8-10.

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