Chapter 2.4, Problem 63AYU

In Problems 64-71, use a graphing utility.

Exploration Graph $y=x^2$. Then on the same screen graph $y=-x^2$. Now try $y=\left|x\right|$ and $y=-\left|x\right|$. What do you conclude?

To determine

To graph: Graph the equations $y = x^2$ and $y = -x^2$. Then observe the pattern from the graph drawn. Predict the graph of $y = \left|x\right|$ and $y = -\left|x\right|$.

Answer to Problem 63AYU

Explanation of Solution

To sketch:

Graph the following equation with the graphing utility:

1. $y = x^2$

2. $y = -x^2$

Interpretation:

The equation $y = x^2$ is an open upwards parabola with the vertex point $\left(0, 0\right)$. And the equation $y = -x^2$ is an open downwards parabola with the vertex point $\left(0, 0\right)$.

Therefore, as the absolute value function $y = \left|x\right|$ open upwards and lies in the quadrant I and II, the absolute value function $y = -\left|x\right|$ open downwards and lies in the quadrant III and IV.

That is, the graph must be like follows: