### 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: $A=LW$

- 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 $a+bi,$ where
*a*is the real part and $b$ 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 in quadratic form
- 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 $\mathrm{-1}$ : $i=\sqrt{\mathrm{-1}}.$

- 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, $\left(x,y\right)$

- origin
- the point where the two axes cross in the center of the plane, described by the ordered pair $\left(0,0\right)$

- 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: $P=2L+2W$

- 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

- quadrant
- one quarter of the coordinate plane, created when the axes divide the plane into four sections

- quadratic equation
- an equation containing a second-degree polynomial; can be solved using multiple methods

- quadratic formula
- a formula that will solve all quadratic equations

- radical equation
- 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 ${x}^{2}$ 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: $V=LWH$

*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