Algebra One Dictionary

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1 Algebra One Dictionary Page 1 of 17

2 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable. All Reals The answer when variables cancel and the numbers left are the same. x + 3 = 3 + x 3 = 3 Area of circle pi multiplied by the square of the radius. A = πr! Area of a rectangle Length multiplied by width. A = lw Area of a triangle one half of the base times the height. A =!! bh Arithmetic Sequence - a sequence in which the difference between terms is constant; generated using a common difference Associative Property - For all real numbers a,b, and c, their sums or product are always the same regardless of their grouping. i.e. (a + b) +c = a + (b + c) (a b) c = a (b c) Asymptote - An asymptote is an invisible line that the graph approaches but never crosses. Asymptotes are written as equations of lines. Average Rate of Change -the ratio of the difference in the dependent variable to the difference in the independent variable. B Base of the exponent -the number or expression that is used as a factor in a repeated multiplication In the expression 3x 2, x is the base. Binomial a polynomial with two terms. 3x 2 + 4x Page 2 of 17

3 Box and Whisker Plot a graph that displays the highest and lowest quarters of data as whiskers and the middle two quarters of data as a box, and the median. C Circumference of a circle the diameter of a circle multiplied by pi. C = πd or C = 2πr Coefficient - A number that is multiplied with a variable; the number in front of a variable. 4x, where 4 is the coefficient Coincide- two or more graphs that have all points in common. (The lines appear as 1 line on the graph) Common Difference - The difference between consecutive terms of an arithmetic sequence or the generator of the sequence. Common Ratio another name for the multiplier or generator of a geometric sequence; see multiplier Commutative Property- states that two or more numbers can be added or multiplied in any order and still arrive at the same sum or product = = 3 8 Compound interest - Interest that is paid on both the principal and the previously accrued interest. Consecutive - Numbers which follow each other in order, without gaps, from smallest to largest. 12, 13, 14 and 15 are consecutive numbers. 22, 24, 26 and 28 are consecutive even numbers. Consistent A system of equations that has only one solution. The solution is an ordered pair. It is the ordered pair where the two lines cross. (2, 5) Page 3 of 17

4 Constant -a term that is a number with no variable. Coordinate Plane -formed by a horizontal number line called the x-axis and a vertical number line called the y-axis. Correlation Coefficient (r) The measure of linear association between two sets of data, this number always lies between -1 and would be a strong correlation.623 would be not so strong of a correlation D Degree (of a Monomial) Found by adding together all the powers of the variables in that monomial. 8x 3 y the degree is 4 Degree (of a Polynomial) The highest power of any term of the polynomial. 8x 3 y + x 2 y 3 xy the degree is five Dependent variable a variable whose value depends on the value of another variable y = 8x 3 1 y is the dependent variable Difference -an answer to a subtraction problem Difference of Squares- A polynomial that can be factored as the product of the sum and difference of two terms. The general pattern is x 2 y 2 = (x + y)(x y) x 2 4 = (x + 2)(x 2) Direct Variation - a relationship between inputs and outputs in which the ratio of inputs and outputs is always the same. B = Ak or B / A = k where k is a constant number and A and B are the two variables. Page 4 of 17

5 Discriminant b 2 4ac The result tells you how many solutions there are to your quadratic equation. Positive perfect square means two rational solutions, Positive non-perfect squares means two irrational solutions, Negative number means no solutions, Zero means one rational solution. x 2 + 2x + 3 a = 1, b = 2, c = 3, discriminant = -8; 0 solutions Distributive Property- if you multiply a sum by a number, you will get the same answer if you multiplier each addend by that number and then add the products 4(7+6) = 4(7)+4(6) Domain all possible x values of a function. E (3, 4), (5, 1), (8, -2) Domain: {3, 5, 8} Equation - A comparison of quantities, terms or expressions that states they are equal (=) to each other Equal Values Method- a method used for solving systems of equation in which both equations are solved for the same variable and then set equal to each other and solved for the other variable. Elimination Method- a method used for solving systems of equation in which a variable is eliminated by adding or subtracting one equation from the other. 2x + 3y = 12 4x 3y = 6 6x = 18 Exponential Function y = ab x + c, where a is the initial value, b is positive and is the multiplier, and y = c is the equation of the horizontal asymptote Evaluate To work out or solve a problem. To find the value of an expression by substituting quantities for the variables. Even Function - A function with a graph that is symmetric with respect to the y-axis. A function is even if and only if f( x) = f(x). Page 5 of 17

Exponent -a number or a variable that represents the number of times a base is used as a factor in a repeated multiplication Exponential decay- occurs when b < 1.

6 Exponent -a number or a variable that represents the number of times a base is used as a factor in a repeated multiplication Exponential decay- occurs when b < 1. Lower values of b decrease at a faster rate Exponential function - y = ab x + q, where a is the initial value, b is positive and is the multiplier, and y = q is the equation of the horizontal asymptote. Exponential growth- occurs when b >1. Higher values of b increase at a faster rate Expression - a combination of terms separated by a plus or minus sign F Factor - two numbers that are multiplied. 1, 2, 3, 4, 6, and 12 are factors of 12 Factor (of a polynomial)- When two or more algebraic expressions are multiplied together each of the expressions is a factor of the product. x 2 is a factor of -17x 2 y 3, because (x 2 )(-17y 3 ) = -17x 2 y 3 Factored Form- A quadratic equation in the form a(x + b)(x + c) = 0, where a is nonzero, is said to be in factored form. -7(x + 2)(x 1.5)=0 FOIL Method - A method to multiply binomials: First, Outside, Inside, Last. (x + 2)(x + 3) Function a relationship in which each input has only one output A function is like an input/output machine. It repeats a rule to determine how each input will be changed to produce each output. Page 6 of 17

7 G Generic Rectangle- a diagram used to show distributive property Geometric Sequence a sequence that is generated by a multiplier; each term can be found by multiplying the previous term by a constant Graphing Method a method used for solving systems of equation in which both equations are graphed and the point of intersection is identified. H Half-life - When material decays, the half-life is the time it takes until only half the material remains Horizontal Line A line that has a slope that is equal to zero. It is parallel to the horizon. I Identity Property- The sum of any number and ZERO is that number. The product of nay number and ONE is that number 4+0 = 4 4(1)=4 Independent variable a variable whose value does not depend on the value of another variable. Indirect Variation - a relationship between two variables in which a change in one variable results in an inverse, or reciprocal, change in the other. If one variable is multiplied by 3, the other is divided by 3. A x B = k or B = k / A where k is a constant number and A and B are the two variables. Inequality- a mathematical sentence that shows the relationship between quantities that are not equivalent using the,, >, or < symbols Page 7 of 17

8 Initial Value - the first term of a sequence; the b in the equation, the y intercept, where x = 0, starting point in word problems. Integer -consisted of negative and positive whole number, including 0 Irrational Number a number that cannot be expressed as a ration of two integers, or as a repeating or terminating decimal or π = JK L Let statement- a statement the defines a variable for an unknown quantity. Example- Let x = # of people going to the movies Like Terms Terms that have the same variable and exponent. 3x 3 y and -24x 3 y Linear Equation an equation in which the input variable has an exponent of 1. Graphs as a line. y = x + 3 Linear Regression (Line of Best Fit) - The most accurate trend line on a scatter plot. It is used to make predictions. y = x + 75 S c i e n c e S c o r e s Math and Science Scores Math Scores Page 8 of 17

9 Local Maximum - The highest point within a given range. Local Minimum - The lowest point within a given range. M Maximum the largest y value of a function. Mean- the sum of all data in a set divided by the number of data items Median middle item in a data set when ordered from least to greatest Minimum the smallest y value of a function. Page 9 of 17

10 Mode- the item that appears most often in a data set Monomial a polynomial with one term. 3x 3 y, -8, 10m, 45cd, 4 x, and many more 5 Multiplier the number you can multiply by in order to increase or decrease an amount by a given percentage in one step. For example, to increase a number by 4%, the multiplier is The multiplier for decreasing by 4% is N Negative Correlation - Relationship between 2 sets of data where 1 set decreases as the other increases. Negative Exponent It equals its reciprocal with a positive exponent. 5!1 = 1 5 or 2 3!2 = No Correlation - There does not appear to be a relationship between two sets of data. Page 10 of 17

11 No Solution When graphing, these lines are parallel. Numerical Expression -An expression that contains only numbers and operations. O Odd Function - A function with a graph that is symmetric with respect to the origin. A function is odd if and only if f( x) = f(x). Order of Operations The order in which operations should be done. PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction Ordered Pair -a pair of numbers that can be used to locate a point in a coordinate plane. The first number is the x-coordinate, and the second number is the y-coordinate Origin -the point (0,0) where the x-axis and the y-axis intersect in a coordinate plane. Page 11 of 17

12 P Parabola The graph of a quadratic equation. Parallel Lines- two or more lines that do not intersect and have the same slope. y = x + 5 y = x 3 Both lines have a slope of one. Parameter - In equations like y = mx + b, where x and y represent the input and output, m and b are referred to as parameters. Parameters are replaced with specific values. Perfect Square Trinomial- Trinomials of the form a 2 x 2 + 2abx + b 2, where a and b are nonzero real numbers, are known as perfect square trinomials and factor as (ax + b) 2. The perfect square trinomial 9x 2 24x + 16 can be factored as (3x 4) 2 Perpendicular Lines - Lines whose slopes are negative reciprocals. Their lines meet to form right angles. m = ½ m = -2 Page 12 of 17

Piecewise Function - A function that uses different formulas for different parts of its domain. Point of Intersection- the point where 2 lines cross each other.

-6x 3 - x 2 + 2x + 3 Positive Correlation - The relationship between two sets of data in which both sets increase. Power an expression made up of an exponent and a base.

13 Piecewise Function - A function that uses different formulas for different parts of its domain. Point of Intersection- the point where 2 lines cross each other. (solution to the system of equations) Polynomial an expression that can have constants, variables, and exponents combined using addition and subtraction. -6x 3 - x 2 + 2x + 3 Positive Correlation - The relationship between two sets of data in which both sets increase. Power an expression made up of an exponent and a base. x 2, where x is the base and 2 is the exponent Product -an answer to a multiplication problem Q Quadrant -four regions into which a coordinate plane is divided by the x-axis and the y-axis II I III IV Page 13 of 17

14 Quadratic Equation- An equation that can be written in the form ax 2 + bx + c = 0, where a, b, ad c are real numbers and a is nonzero. x 2 + 3x + 1 = 0 Quotient -an answer to a division problem R Range the difference between the greatest data value and the least data value in the set Range (of a function) all possible y values of a function. (3, 4), (5, 1), (8, -2) Range: {-2, 1, 4} Rational exponent - Raising a number to a fractional exponent indicates a power as well as a root. Rational Number any number that can be expressed as a ratio of two integers Root (also called a zero) in a quadratic expression, is a value of x that makes the expression equal to zero. The roots or zeros are the solutions when the expression is set equal to zero. The x-intercepts of any quadratic function are roots. S Scatter Plot -the graph of a collection of ordered pairs (x,y) Sequence a function in which the independent variable is a positive integer; usually written as a list of numbers Page 14 of 17

15 Sequence Generator tells what you do to each term in a sequence to get the next term; only tells you the next term if you know one term; is the common difference in an arithmetic sequence and the multiplier in a geometric sequence Simplify - Perform operations, combine like terms and apply properties to an expression to make it easier to use. Slope the measure of steepness of a line. (m =!"#$!"# ;!!!! ; Average Rate of Change). Formula for slope: m =!!!!!!!!!! Slope-Intercept Form of a Linear Function - y = mx+b where m is slope and b is y-intercept. Square Root-one of the two equal factors of a number 16 = 4 x 4 or 16 = -4 x -4 so 4 and -4 are square roots of 16 Solution- the number or numbers that when substituted into an equation or inequality make a true statement. Standard Form of a Linear Function - Ax + By = C where A, B, and C are Real numbers and A and B cannot be zero. Standard Form of a Quadratic Expression- A quadratic expression in the form of ax 2 + bx + c is said to be in standard form. Substitution Method One equation is solved for a variable and substituted into the other. 3x 4y = 16 3x 4(x + 7) = 16 y = x + 7 System of Equations- a set of equations with the same variables working together to solve a given situation. 2x + 3y = 12 4x 3y = 6 T Term - A number, variable, or any combination of numbers and variables joined by multiplication or division. 2x, 3y, 12 Page 15 of 17

16 Term Number In a sequence, a number that gives the position of a term in the sequence Trinomial a polynomial with three terms. x 2 + 5x + 6 Trinomial Square The square of a binomial. U (x + 3) 2 = x 2 + 6x + 9 Undefined A vertical line has an undefined slope. If something is divided by zero than it is undefined. V Variable - A symbol, usually a letter, used to represent a quantity that can change. Vertex- The vertex of a parabola is the highest or lowest point on the parabola (depending on the parabola s orientation). Vertical Line A line whose slope is undefined. At right angles to the horizon. See the picture for undefined. Vertex Form (also called Graphing Form)- A form of the equation of a function or relation that clearly shows key information about the graph. For example: the vertex or graphing form for the general equation of a quadratic function is y = a(x h) 2 + k. The vertex (h, k), orientation (whether a is positive or negative), and amount of stretch or compression based on a > 1 or a < 1 appear in the equation. Page 16 of 17

17 W X X-axis -the horizontal number line in a coordinate plane X-intercept where a graph crosses the x-axis, when y = 0 (3, 0) Y Y-axis - the vertical number line in a coordinate plane. Y-intercept where a graph crosses the y-axis, when x = 0 (0, 3) Z Zero Exponent Any term raised to this power will equal one. 5 0 = 1 OR 5abc 24xyz 0 = 1 Zero Product Property The Zero Product Property sates that when the product of two or more factors is zero, one of these factors must equal zero. That is, if a b = 0, then either a = 0 or b = 0 (or both). The Zero Product Property can be used to solve factorable quadratic equations. If (x + 4)(2x 3) = 0, the x + 4 = 0 or 2x 3 = 0 (or both) Page 17 of 17

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations. Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic