### Home > AC > Chapter 3 > Lesson 3.1.7 > Problem3-66

3-66.

For each rule below, make a table of $x$- and $y$-values and then graph the rule on graph paper. Label each graph with its equation. 3-66 HW eTool (Desmos). Homework Help ✎

1. $y=x^2$

Substitute positive and negative values for $x$ and solve for $y$.

1. $y=−x^2$

1. Compare the graphs. What do you notice?

What are the shapes of the graphs of part (a) and part (b)?

The $y=x^2$ graph points upward and the $y=−x^2$ graph points downward.

2. For the graph of $y=x^2$, estimate the $x$-values corresponding to $y=5$.

Estimate the $x$-value where the line $y=5$ intersects the parabola. (See graph for the line $y=5$)

3. For the graph of $y=−x^2$, estimate the $x$-values corresponding to $y=−10$.

See the hint in part (d).

Complete the tables in the eTool below.
Click the link at right for the full version of the eTool: AC 3-66 HW eTool