In this section, you will solve square root equations using graphs. The idea is the same as finding solutions in a table. First, you need to define your variables, and then you will find a point on the graph just as you did with the table. A benefit to looking at a graph is that you can easily see the domain and range of the function that you cannot always determine by looking at a table.

Let's look at example 2 from section 1 again.

The equation y = 8√x gives the speed in feet per second of an object in free fall after falling x feet.

First, let's look at the graph of this equation. You can use your graphing calculator, or you can use the following GCalcx applet to graph this equation. If you're using the applet, enter 8sqrt(x) into the space next to y(x)= in the applet to graph the equation. Once you have graphed it, click on the negative magnifying glass on the left 4 or 5 times to zoom out, and get a good window. Also, change the X gap and Y gap at the bottom right to 1.

To open the applet, click on the image below.

See if the answers you got in section 1 match the graph.

1. What is the speed of a free falling object after it has fallen 16 ft?

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   Check Your Answer

   32 ft/s

2. How far has an object fallen if it is falling at a speed of 16 ft/s?

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   Check Your Answer

   4 ft

You should have gotten the same answers as you did in section 1 for this example.

3. What other information can you get from your graph?

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   Possible Answer

   There are many other points on the graph. A couple of them are at 36 ft, the object was falling at 48 ft/s, or an object that was falling at 24 ft/s had fallen 9 feet.

Reading a graph is just another way to find solutions and solve equations. Specifically for this lesson, you are investigating square root equations. In the next section, you will review what you just learned and tie both methods together.