#### Math - 2017-18

# 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.3The student willsolvea) absolute value linear equations

~~and inequalities~~;

**Bloom's Level:** Apply

*Adopted: 2009*

### 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.4a_{1} **Solve**
absolute value equations and inequalities algebraically and graphically.

·
AII.3a_{1} **Solve**
absolute value linear equations or inequalities in one variable
algebraically.

AII.4_{1} **Apply**
an appropriate equation to **solve** a
real-world problem.

·
AII.3_{1} **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*