In the first section, we started with the parent square root function, y = √x. This equation is in algebraic form. Given any square root function in algebraic form, you can represent the same function easily in other forms.

Let's begin with another square root function in algebraic form.

Example 1: Given y = √(3x + 4),

1. Write this equation in tabular form.
1. Make a table of values to represent this function. The first row is completed for you. To check the rest of your answers, click on each box in the table below. Copy and paste the equation along with your table in your tool.
   

   X	Process	Y
   - four-thirds 4 3	√3(- four-thirds 4 3 ) + 4	0
   -1	Interactive button. Assistance may be required. _____________ √3(-1) + 4	Interactive button. Assistance may be required. _____________ 1
   0	Interactive button. Assistance may be required. _____________ √3(0) + 4	Interactive button. Assistance may be required. _____________ 2
   4	Interactive button. Assistance may be required. _____________ √3(4) + 4	Interactive button. Assistance may be required. _____________ 4

2. Why do you think these specific x values were chosen for the table? Answer in your Notes Section. To check your answer, Interactive popup. Assistance may be required. click here. These x values result in friendly y values, but any value of x can be used. Close
3. Which of the points in the table are critical points? To check your answer, Interactive popup. Assistance may be required. click here. The first point (- four-thirds 4 3 ,0) is the starting point of the graph. It is also the x-intercept. The point (0,2) is the y-intercept. These are critical points on the graph. Close
2. Write the equation in graphical form.

1. To go from algebraic form to graphical form, the same process applies. Knowing what you learned in Algebra II, Module 3, Lesson 3, we can apply your knowledge of transformations to identify the graph's starting point. First we need to get the equation into the form y = a√(x − h) + k.

   Follow through the steps below by clicking on the equal signs to reveal each step.

   y = √3x + 4

   y Interactive button. Assistance may be required. = = √3(x + four-thirds 4 3 )

   y Interactive button. Assistance may be required. = = √3 * √x + four-thirds 4 3

2. Describe the translation. Interactive popup. Assistance may be required. Check Your Answer. It's a vertical stretch by a factor of √3 and a horizontal shift to the left - four-thirds 4 3 units. Close
3. What is the graphs starting point? Interactive popup. Assistance may be required. Check Your Answer. (- four-thirds 4 3 , 0) Close
4. Now we just need two more points to complete our graphs. In order to do this, we want to look for easy numbers to graph. That is, when we plug in an integer for x, we get an integer for y, and not a decimal. Looking at the original equation again, y = √3x + 4, think about what integers you could substitute in for x, to get a "nice" number for y. The numbers and critical points you found in the table would be good numbers to plot.
5. Click below to animate the graph.