To graph the function $y = -x^2$ using the given table of values, we need to plot the points provided in the tables on the coordinate grid. Here are the points from the table:

Points from the Table:

• For $x = -10$, $y = -100$
• For $x = -9$, $y = -81$
• For $x = -8$, $y = -64$
• For $x = -7$, $y = -49$
• For $x = -6$, $y = -36$
• For $x = -5$, $y = -25$
• For $x = -4$, $y = -16$
• For $x = -3$, $y = -9$
• For $x = -2$, $y = -4$
• For $x = -1$, $y = -1$
• For $x = 0$, $y = 0$
• For $x = 1$, $y = -1$
• For $x = 2$, $y = -4$
• For $x = 3$, $y = -9$
• For $x = 4$, $y = -16$
• For $x = 5$, $y = -25$
• For $x = 6$, $y = -36$
• For $x = 7$, $y = -49$
• For $x = 8$, $y = -64$
• For $x = 9$, $y = -81$
• For $x = 10$, $y = -100$

Steps to Plot:

1. Select at least five points from the above list to plot on the coordinate plane.
2. Points closer to the origin (0, 0) are easier to plot manually.
3. Recommended points for clarity might include: $(-3, -9)$, $(-2, -4)$, $(-1, -1)$, $(0, 0)$, $(1, -1)$, $(2, -4)$, and $(3, -9)$.
4. Once you have plotted the points, draw a smooth curve connecting them to represent the parabola.

Would you like a detailed example of plotting these points on a coordinate plane or any further assistance with another part of the problem? Let me know if you need additional help.

Questions for You to Ask Next:

1. How do I find the vertex of a parabola given the quadratic function?
2. How do I determine the axis of symmetry for the function $y = -x^2$?
3. What are the steps to identify the direction of opening of a parabola?
4. Can you explain how to find the roots of the quadratic equation $y = -x^2$?
5. How do transformations affect the graph of a quadratic function?

Tip:

When graphing quadratic functions, always remember to identify key features such as the vertex, axis of symmetry, and direction of opening to understand the shape and position of the parabola.