College Algebra 2e

# Key Terms

### Key Terms

absolute value equation
an equation in which the variable appears in absolute value bars, typically with two solutions, one accounting for the positive expression and one for the negative expression
area
in square units, the area formula used in this section is used to find the area of any two-dimensional rectangular region: $A=LW A=LW$
Cartesian coordinate system
a grid system designed with perpendicular axes invented by René Descartes
completing the square
a process for solving quadratic equations in which terms are added to or subtracted from both sides of the equation in order to make one side a perfect square
complex conjugate
a complex number containing the same terms as another complex number, but with the opposite operator. Multiplying a complex number by its conjugate yields a real number.
complex number
the sum of a real number and an imaginary number; the standard form is $a+bi, a+bi,$ where a is the real part and $b b$ is the complex part.
complex plane
the coordinate plane in which the horizontal axis represents the real component of a complex number, and the vertical axis represents the imaginary component, labeled i.
compound inequality
a problem or a statement that includes two inequalities
conditional equation
an equation that is true for some values of the variable
discriminant
the expression under the radical in the quadratic formula that indicates the nature of the solutions, real or complex, rational or irrational, single or double roots.
distance formula
a formula that can be used to find the length of a line segment if the endpoints are known
equation in two variables
a mathematical statement, typically written in x and y, in which two expressions are equal
equations with a power other than 2 but with a middle term with an exponent that is one-half the exponent of the leading term
extraneous solutions
any solutions obtained that are not valid in the original equation
graph in two variables
the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane
identity equation
an equation that is true for all values of the variable
imaginary number
the square root of $−1 −1$ : $i= −1 . i= −1 .$
inconsistent equation
an equation producing a false result
intercepts
the points at which the graph of an equation crosses the x-axis and the y-axis
interval
an interval describes a set of numbers within which a solution falls
interval notation
a mathematical statement that describes a solution set and uses parentheses or brackets to indicate where an interval begins and ends
linear equation
an algebraic equation in which each term is either a constant or the product of a constant and the first power of a variable
linear inequality
similar to a linear equation except that the solutions will include sets of numbers
midpoint formula
a formula to find the point that divides a line segment into two parts of equal length
ordered pair
a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, $( x,y ) ( x,y )$
origin
the point where the two axes cross in the center of the plane, described by the ordered pair $( 0,0 ) ( 0,0 )$
perimeter
in linear units, the perimeter formula is used to find the linear measurement, or outside length and width, around a two-dimensional regular object; for a rectangle: $P=2L+2W P=2L+2W$
polynomial equation
an equation containing a string of terms including numerical coefficients and variables raised to whole-number exponents
Pythagorean Theorem
a theorem that states the relationship among the lengths of the sides of a right triangle, used to solve right triangle problems
one quarter of the coordinate plane, created when the axes divide the plane into four sections
an equation containing a second-degree polynomial; can be solved using multiple methods
a formula that will solve all quadratic equations
an equation containing at least one radical term where the variable is part of the radicand
rational equation
an equation consisting of a fraction of polynomials
slope
the change in y-values over the change in x-values
solution set
the set of all solutions to an equation
square root property
one of the methods used to solve a quadratic equation, in which the $x 2 x 2$ term is isolated so that the square root of both sides of the equation can be taken to solve for x
volume
in cubic units, the volume measurement includes length, width, and depth: $V=LWH V=LWH$
x-axis
the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right
x-coordinate
the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin
x-intercept
the point where a graph intersects the x-axis; an ordered pair with a y-coordinate of zero
y-axis
the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top
y-coordinate
the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin
y-intercept
a point where a graph intercepts the y-axis; an ordered pair with an x-coordinate of zero
zero-product property
the property that formally states that multiplication by zero is zero, so that each factor of a quadratic equation can be set equal to zero to solve equations
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