Topic: Solutions of Radical Equations

Level:

Algebra 2

TI-81/82 Proficiency:

Some Previous Experience with Graphing Functions

Menus/Keystrokes Needed:

Students should be familiar with how to define functions to be graphed using the Y= key and how to set up a standard viewing screen using Zoom 6.

Notes to Teachers:

Students ought to be previously taught to solve radical equations. The first problem was a demonstration, the second was done together with the students. Students were then assigned to complete a lab sheet for each of the three problems attached, completing the assignment outside of class.

Demonstration Problem:

1. Solve algebraically:

  1. Isolate the radical.
  2. Square both sides.
  3. Bring all terms to one side.
  4. Factor.
  5. Set each factor equal to zero.
  6. Check each solution.

2. Graph f( x) =
The zero(s) are:______________________ .

3. Graph the equation
The zero(s) are: ____________________ .

4. Are the two graphs the same? Do they both have the same zeros (roots)?

5. What does this suggest about the solutions to the original equation?

Class Problem

1. Solve algebraically:

2. Check your solutions algebraically.

3. Graph the function:
The function has zero(s) at ___________.

4. Graph the function: g(x) = x*x - 10x + 9

The function has zero(s) at ___________.

Conclusions:

  1. Does f have any extraneous solutions? ______________
  2. The domain of f is _________________ .
  3. The domain of g is _________________ .
  4. Is it possible to predict from the equation whether extraneous solutions will exist? How would you determine is a solution is extraneous?


Use the following Lab Sheet to solve these three problems:

RADICAL EQUATIONS LAB SHEET

Name_________________________________ Date____________________

1. Write the equation being solved here. _________________________

2. Solve the equation algebraically.

3. Set the equation in #1 equal to f(x) and graph the function f(x).

3a. The zero(s) are ___________________.

4. Set g(x) equal to the equation that you set equal to zero in your work in #2 and graph the function g(x).

4a. The zero(s) are ____________________.

5. The solution to the equation in #1 is: ____________________.

6. Does the equation in #1 have any extraneous solutions? _____________.

EXPLORE FURTHER:

Is it possible to predict from the equation whether extraneous solutions will exist? How would you determine is a solution is extraneous?

Eileen Robinson
Fort Lee High School
Fort Lee, New Jersey 07024