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2.4            Vocabulary for the Quadratic Inequalities

 

Critical Numbers

Inputs that make a function output 0 or undefined.    Used as endpoints on a sign chart

 

Factor     A factor is a number, variable or quantity that is being multiplied.

 

Two factors:                                      Three factors:        

Two factors:        2 (x+1)                          Two factors:      (x-3)(x2 + 2x + 1)

 

Inequality

An algebraic statement that a quantity is greater than or less than another quantity.  Symbols used are  

.

 

Interval

A set consisting of all the numbers in between a pair of given numbers;  a line segment representing such a set;   a portion of the real number line.

 

Irrational number

A real  number that is not rational.  As a decimal, an irrational number is non-terminating and non-repeating.  Some common irrational numbers are Click here to review all subsets of real numbers.

          In a polynomial, the coefficient of the term with the highest degree.

 

 

                  

x-intercept

The x-coordinate of a point where a graph intersects the x-axis.   Since the point is on the x-axis, the y-coordinate is zero.

 

Rational number

A number that can be written in the form , where a and b are integers and . As a decimal, rational numbers either terminate (end) or repeat.  Click here to review all subsets of real numbers.

 

Revenue

The amount of money generated from the sale of goods or services.

 

Sign chart

An organizational tool used to keep track of the sign (positive or negative) of the function outputs in certain intervals.  Normally, the endpoints of the intervals are the critical numbers  of the function.

 

Test number

A number arbitrarily chosen in an interval to test whether the outputs in the interval are positive or negative.

 

Zero of a function

An input value for the function which has  0 for the output.  In conventional usage, it’s a value for x  which gives 0 as the y-value (output).  For example the numbers 2 and -2 are zeros of the function  because .  On the graph of a function, a zero is an x-intercept.

 

                              

 

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