# AII.4a and *AII.3a - Absolute Value Equations

AII.4    The student will solve, algebraically and graphically,

a)  absolute value equations and inequalities;

Graphing calculators will be used for solving and for confirming the algebraic solutions.

AII.3  The student will solve

a)  absolute value linear equations and inequalities;

Bloom's Level:  Apply

### BIG IDEAS

• I can find how far and how fast a bus travels, the number and combinations of fruits that can be purchased, and how long it takes to drain a swimming pool.
• I will be able to write symbolic representations of the way numbers behave and will know that in order to maintain equality, an operation performed on one side must also be performed on the other side.

### UNDERSTANDING THE STANDARD

• A quadratic function whose graph does not intersect the x-axis has roots with imaginary components.
• The quadratic formula can be used to solve any quadratic equation.
• The value of the discriminant of a quadratic equation can be used to describe the number of real and complex solutions.
• The definition of absolute value (for any real numbers a and b, where b ≥ 0, if  |a| = b, then a = b or a = - b) is used in solving absolute value equations and inequalities.
• Absolute value inequalities can be solved graphically or by using a compound statement.
• Real-world problems can be interpreted, represented, and solved using equations and inequalities.
• The process of solving radical or rational equations can lead to extraneous solutions.
• Equations can be solved in a variety of ways.
• Set builder notation may be used to represent solution sets of equations and inequalities.

·  The definition of absolute value (for any real numbers a and b, where

b  0, if |a|= b, then a = b or a = − b) is used in solving absolute value equations and inequalities.

·  Absolute value inequalities in one variable can be solved algebraically using a compound statement.

### ESSENTIALS

Equations

AII.4a1  Solve absolute value equations and inequalities algebraically and graphically.

·  AII.3a1  Solve absolute value linear equations or inequalities in one variable algebraically.

AII.41  Apply an appropriate equation to solve a real-world problem.

·  AII.31  Solve equations and verify algebraic solutions using a graphing utility.

### KEY VOCABULARY

absolute value equations, absolute value inequalities, quadratic equation, complex numbers, rational algebraic expression, radical expression, algebraically, graphically, quadratic function, discriminant, real solutions, complex solutions, monomial, binomial, denominator, quadratic formula, verify, completing the square

Updated: Oct 27, 2017