Vocabulary & Definitions Algebra 1 Midterm Project

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1 Vocabulary & Definitions Algebra 1 Midterm Project Associative Property When you are only adding or only multiplying, you can group any of the numbers together without changing the value of the expression. Commutative Property You can add numbers or multiply numbers in any order without changing the value of the expression. Distributive Property Expression Translation Variable Evaluate Exponent Sum Difference Product When you multiply a term by a sum or difference in ( ), you can multiply by that sum or difference, or by each term inside the ( ) separately, then add or subtract the products afterwards, without changing the value of the expression. A mathematical statement that contains operations, numbers and/or variables. 1) To change an algebraic expression into words and vice versa. 2) To transform a graph by shifting or sliding all the points the same distance in the same direction. A letter used to represent a value that can change. To find the value of an expression by simplifying; numbers are substituted for variables if variables are part of the expression. The power to which a base is raised to; tells how many times the base is multiplied by itself. The answer to an addition problem. The answer to a subtraction problem. The answer to a multiplication problem.

2 Quotient The answer to a division problem. Absolute Value The distance a number is from zero on the number line; always a positive value. Radical Symbol The grouping symbol used to denote a square root of the expression underneath. Coefficient Equation Inequality Term Like Terms A number multiplied by a variable the number co nnected to a variable by multiplication. A variable written without a coefficient, always has an invisible coefficient of 1. A mathematical statement that two expressions are equal to each other. A mathematical statement that two quantities or expressions are NOT equal, and have infinite solutions with boundaries; the quantities are compared by using one of the symbols < > A monomial; the parts of an expression to be added or subtracted. Terms that contain the same variable(s) raised to the same power(s). Verbal Expression An expression that uses words instead of mathematical symbols and numbers. Algebraic Expression Solution Solution Set Zero pair Simplify An expression that contains at least one variable, and sometimes symbols and numbers. A value or values that make the equation true. The SET of values that make the equation true. A pair of numbers that combine to equal zero a positive and negative of the same number add to zero. To perform all indicated operations; to make simpler.

3 Coordinate Plane A graph where 2 perpendicular number lines intersect to form 4 quadrants. x axis The horizontal number line on a coordinate plane. y axis The vertical number line on a coordinate plane. Origin The point of intersection of the 2 axes on a coordinate plane; the ordered pair ( 0, 0 ) Ordered Pair The x coordinate and y coordinate that describe the location of a point on a coordinate plane. Quadrant The 4 parts of a coordinate plane formed by the 2 axes; labeled as I, II, III and IV. Input The x value of a function; the independent variable; the set of values that are the Domain. Output The y value of a function; the dependent variable; the set of values that are the Range. Solution The value of a variable that makes an equation true. Relation A set of ordered pairs typically written in list form between set brackets Relations may also be shown as mapping, as a table or as points on a coordinate plane. Function A special type of relation that pairs each Domain value with exactly one Range value. Constant A term whose value does not change. Continuous Graph A graph made up of connected points that form lines or curves Discrete Graph A graph made up of unconnected points; separate distinct points

4 Dependent Variable The variable represented by y in a function; Independent Variable Domain Range The variable represented by x in a function. The set of all of the 1st coordinates in a relation; all of the x s ; the independent variables. The set of all of the 2 nd coordinates in a relation; all of the y s ; the dependent variables. Function Notation f(x) Intercept x intercept y intercept Written as f(x) ; Read as the function of x or f of x ; function notation; a fancy way of saying y The point where two lines intersect; the y intercept is where a graph intersects the y axis; the x intercept is where a graph intersects the x axis. The point where a graph intersects the x axis; the ordered pair ( x, 0 ) where y = 0. The point where a graph intersects the y axis; the ordered pair ( 0, y ) where x = 0. Zeros of a Function The point or points on the graph of a parabola where y = 0; where the parabola crosses the x axis; also called roots. Roots of a Function The point or points on the graph of a parabola where crosses the x axis; where y = 0; also called zeros Linear Function A function whose graph forms a line and whose points represent a constant rate of change. Quadratic Function A function whose graph forms a parabola.

5 Parent Function Parabola The simplest form of the function in that family. The "U" shaped graph of a quadratic function. Transformation Slope To change the location/position, size or shape of a graph; what we do to a parent function. The ratio the change in y over the change in x values of a function; rise over run ; the steepness of a line. Slopes can be +,, 0 (horizontal), or undefined (vertical). Rate of Change A way of describing slope or constant rate of change. Point Slope Form The form of a linear equation y y 1 = m(x x 1 ) where m is the slope and ( x 1, y 1 ) is a point on the line. Slope Intercept Form The form of a linear equation y = mx + b where m is the slope and b is the y intercept. Standard Form Polynomial Monomial The form of a linear equation Ax + By = C where A, B and C are real numbers and A and B are not both 0. A function is linear if it can be written in this form. A monomial; the sum or difference of monomials. A term; a number; a set of numbers and variables connected by multiplication.