Algebra 2
Solving Absolute Value Equations Algebraically
Vertex form of absolute value equation: [pic]
1. What does a, h, and k control in the equation above?
Graph the following equations on the grid provided. Do not use a calculator!
2. [pic] 3. [pic]
4. Using the graph in #2, how many solutions will there be to the equation[pic]?
5. What are these solutions?
6. Using the graph in #3, how many solutions will there be to the equation[pic]?
7. What are these solutions?
On the previous page, you solved two absolute value equations using a graphical method. While these equations were easy to solve using this graphical method, there are times when it will be easier to use the algebraic method. When using the algebraic method, it is important to remember how many solutions you can get for an absolute value equation.
8. How many solutions will there be for the following systems? Circle the solutions.
a. b.
c.
d. How many possible solutions can an absolute value equation have?
Examples of solving absolute value equations:
a. b.
c. In #8c, we see that the graphs will never meet. There are _______ solutions. Write an equation to show this situation.
Examples as a class:
A) [pic] B) [pic]
C) [pic] D) [pic]
Solving Absolute Value Equations Algebraically cont.
Solve the following equations.
9. [pic]
3. [pic]
5.[pic]
2. [pic]
4. [pic]
6. [pic]
7. [pic]
10. [pic]
8. [pic]
10. [pic]
11. [pic] 12. [pic]
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[pic]
[pic]
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