The task is to graph the equation $y = -x^2$ by plotting at least five points.

Steps to Solve:

1. Understand the equation:
   The equation $y = -x^2$ is a downward-facing parabola because of the negative sign before $x^2$.

2. Choose $x$-values:
   Select at least five $x$-values (e.g., -2, -1, 0, 1, 2).

3. Calculate corresponding $y$-values: Use the equation $y = -x^2$:

   • If $x = -2$, $y = -(-2)^2 = -4$.
   • If $x = -1$, $y = -(-1)^2 = -1$.
   • If $x = 0$, $y = -(0)^2 = 0$.
   • If $x = 1$, $y = -(1)^2 = -1$.
   • If $x = 2$, $y = -(2)^2 = -4$.

4. Plot the points: The points to plot are:

   • (-2, -4)
   • (-1, -1)
   • (0, 0)
   • (1, -1)
   • (2, -4)

5. Sketch the curve:
   Draw a smooth curve through the plotted points to form the parabola.

Would you like a detailed explanation of graphing or need me to generate an image of the graph?

5 Related Questions:

1. How can you verify the symmetry of a parabola around the y-axis?
2. What effect does changing the sign of $x^2$ have on the graph?
3. How do you calculate the vertex of the parabola $y = -x^2 + k$?
4. What happens if you add or subtract constants to $y = -x^2$?
5. How does the steepness of the parabola change if $y = -2x^2$?

Tip:

For any quadratic equation $y = ax^2 + bx + c$, the vertex is given by $x = -\frac{b}{2a}$. This is useful for graphing more complex parabolas!