allows us to add the same amount to both sides of an equation: For all real numbers a, b, and c, if a = b, then a + c = b + c

states that any number plus zero equals that number: For all real numbers a, a + 0 = a

states that every real number added to its additive inverse (or opposite) will equal zero: For all real numbers a, a + (-a) = 0; also called Inverse Property of Addition

states that numbers in an addition sequence can be added in any order, and the value of the expression will not change: For all real numbers a, b, and c, (a + b) + c = a + (b + c)

states that numbers in a multiplication sequence can be multiplied in any order, and the value of the expression will not change: For all real numbers a, b, and c, (ab)c = a(bc)

the value that is raised to a power when a number is written in exponential notation.  In the term 5³, 5 is the base and 3 is the exponent.

a sum of two monomials, such as 3x² + 7

states that when two values are added together, changing their order does not affect their sum: For all real numbers a and b, a + b = b + a

states that when two values are multiplied together, changing their order does not affect their product: For all real numbers a and b, ab = ba

the process of changing a polynomial of the form  into a perfect square trinomial , or

a plane in two dimensions, containing the x- and y-axes, used to map ordered pairs in the form (x, y)

a pair of numbers that identifies a point on the coordinate plane—the first number is the x-value and the second is the y-value

the expression b² – 4ac under the radical in the quadratic formula; the expression can be used to determine the number of real roots the quadratic equation has

states that the product of a number and a sum equals the sum of the individual products of the number and the addends: for all real numbers a, b, and c, a(b + c) = ab + ac

allows us to divide both sides of an equation by the same amount: For all real numbers a, b, and c, if a = b and c is not 0, then

the value that indicates the number of times another value is multiplied by itself in exponential notation. The exponent, also called the power, is written in superscript. In the term 5³, 5 is the base and 3 is the exponent.

a nonlinear function in which the independent value is an exponent in the function, as in y = ab^x

a condensed way of expressing repeated multiplication of a value by itself. Exponential notation consists of a base and an exponent. In the exponential term 5³, 5 is the base and 3 is the exponent. This is a shorthand way of writing 5 • 5 • 5. Also called exponential form.

for any number x, the numbers that can be evenly divided into x are called factors of x. For example, the number 20 has the factors 1, 2, 4, 5, 10, and 20.

an abbreviated way of writing a product of all whole numbers from 1 to a given number, indicated by that number followed by an exclamation point, as in 3! = 3 • 2 • 1

the process of breaking a number down into its multiplicative factors. Every number x has at least the numbers 1 and x as factors.

a math sentence that defines a range of numbers; inequalities contain the symbols <, ≤, >, or ≥

written as y = a(x – p)(x – q), where the x-intercepts are p and q

a nonlinear function in which the reciprocal of the independent variable times a constant equals the dependent variable, as in

states that every real number added to its additive inverse (or opposite) will equal zero: for all real numbers a, a + (-a) = 0; also called Additive Inverse Property

states that any number multiplied by 1 over that number equals 1: For all real numbers a, ; also called Multiplicative Inverse Property

numbers between integers that cannot be written as a ratio of integers (that is, as  where p and q are both integers), the decimal representation of an irrational number is non-repeating and non-terminating

two or more monomials that contain the same variables raised to the same powers, regardless of their coefficients. For example, 2x²y  and -8x²y are like terms because they have the same variables raised to the same exponents.

an inequality represented in a form equivalent to Ax + By > C, where the symbol > could also be <, ≤, or ≥

a number, a variable, or a product of a number and one or more variables with whole number exponents, such as -5,  x, and 8xy³

allows us to multiply both sides of an equation by the same amount: For all real numbers a, b, and c, if a = b, then ac = bc

states that any number times 1 equals that number: For all real numbers a, a • 1 = a

states that any number multiplied by 1 over that number equals 1: For all real numbers a, ; also called Inverse Property of Multiplication

lines that have the same slope and different y-intercepts

any of the squares of the integers. Since 1² = 1, 2² = 4, 3² = 9, etc., 1, 4, and 9 are perfect squares

a trinomial that is the product of a binomial times itself, such as r² + 2rs + s² (from (r + s)²), and r² – 2rs + s² (from (r – s)²)

a form of linear equation, written as, where m is the slope and (x₁, y₁) are the co-ordinates of a point

a monomial or sum of monomials, like 4x² + 3x – 10

a monomial or sum of monomials, like y = 4x² + 3x – 10

a way of describing the exponent in exponential notation. We can say the base is raised to the power of the exponent.  For example we read x⁵ as “x raised to the 5^th power.”

raising a value written in exponential notation to a power as in (x²)³

the formula used to relate the lengths of the sides in any right triangle

an equation that can be written in the form ax² + bx + c = 0 where a ¹ 0. When written as y = ax² + bx + c the expression becomes a quadratic function.

the formula  ; it is used to solve a quadratic equation of the form

a function of the form y = ax² + bx + c where a is not equal to zero

the math symbol , used to denote the process of taking a root of a quantity

a quantity that contains a term with a radical, as in

a way of describing the exponent in exponential notation. We can say the base is “raised to the power” of the exponent.  For example we read x⁵ as “x raised to the 5^th power.”

numbers that can be written as a ratio of integers (that is, as  where p and q are both integers and q ≠ 0)

a number related to another number in such a way that when they are multiplied together their product is 1.  For example, the reciprocal of 7 is  because ; the reciprocal of  is .  It is also called the multiplicative inverse.

any number x multiplied by itself a specific number of times to produce another number, such that in xⁿ = y, x is the nth root of y – for example, because 2³ = 8, 2 is the 3^rd (or cube) root of 8

the x-intercepts of the parabola or the solution of the equation

a convention for writing very large and very small numbers in which a number is expressed as the product of a power of 10 and a number that is greater than or equal to 1 and less than 10 as in 3.2 • 10⁴

the equation for the slope of a line, written as , where m is the slope and (x₁, y₁) and (x₂, y₂) are the coordinates of two points on the line

a linear equation, written in the form y = mx + b, where m is the slope and b is the y-intercept

a linear equation, written as y = mx + b, where m is the slope and b is the y-intercept

a product resulting from binomial multiplication that has certain characteristics. For example x² – 25 is called a special product because both its terms are perfect squares and it can be factored into (x + 5)(x –­ 5).

a linear equation, written in the form Ax + By = C, where x and y are variables and A, B, and C are integers

written as , where x and y are variables and a, b, and c are numbers with a ≠ 0. In the case of a single variable the standard form becomes ax² + bx + c = 0.

allows us to subtract the same amount from both sides of an equation: For all real numbers a, b, and c, if a = b, then a – c = b – c

a value in a sequence--the first value in a sequence is the 1^st term, the second value is the 2^nd term, and so on; a term is also any of the monomials that make up a polynomial

when the quadratic equation is a quadratic function, the vertex form is , where x and y are variables and a, h, and k are numbers – the vertex of this parabola has the coordinates (h, k)

the point where a line meets or crosses the x-axis

the point where a line meets or crosses the y-axis

states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0