In this lesson, you will learn how to solve a square root equation using tables and graphs as well as how these two methods are connected. You will begin by solving using tables first. It's important to understand domain, so that you can determine the appropriate values for your table.
Let's begin with an example.
Example 1: y = √(x + 3)
How do you know what x-values are acceptable for this problem's table?
How do you find the domain?
Find the domain for this problem.
Complete the table below.
You can do so by substituting the values in the X column into the equation above to get the Y values. For example, substituting -3 into the equation gives you y = √(-3 + 3) = √0 = 0. Click in the empty spaces in the Y column to reveal the remaining Y values.
X | Y |
---|---|
-3 | 0 |
-2 | Interactive button. Assistance may be required. _______ 1 |
1 | Interactive button. Assistance may be required. _______ 2 |
6 | Interactive button. Assistance may be required. _______ 3 |
Use the table to answer the following questions.
Can the x-values be less than -3? Why?
As the x-values increase, what happens to the y-values?
Example 2: The equation y = 8√x gives y, the speed in feet per second of an object in free fall after falling x feet.
Which column represents the number of feet the object has fallen? (X or Y)
Which column represents speed a free falling object? (X or Y)
Use the same table to find the height of a free falling object when it has a speed of 16 ft/s.
Using a table is one way to solve square root functions. In the next section, you will solve square root equations by using graphs.