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GRE Math Terms: Algebra
Algebraic Terms for the Quantitative Reasoning Section of the GRE. For the best results, read the GRE math review before using these flash cards.
179
Mathematics
Not Applicable
10/31/2012

Term
 Term
Definition
 A single number or variable, or numbers and variables multiplied together or divided by one another.2x and 5z² are both terms.8/(n+p) is also a term.2x + 7p + x/2 contains three terms: 2x, 7p, and x/2.
Term
 What Distinguishes Algebra from Arithmetic?
Definition
 The presence (or use) of variables.
Term
 Variable
Definition
 A letter or symbol that represents a quantity whose value is unknown.Usually expressed as a lowercase italic letter.
Term
 Algebraic Expression
Definition
 A term or group of terms which has one or more variables.2x, 5z², 8/(n+p), and 2x + 7p + x/2 are all algebraic expressions.
Term
 Like Terms
Definition
 Two (or more) terms with the same variable.
Term
 Constant Term
Definition
 A term with no variable.
Term
 Coefficient
Definition
 A number that is multiplied by variables in a term.For 5x, 5 is the coefficient.
Term
 What is 3x+6x?
Definition
 9x.When adding algabraic expressions, like terms can combined by simply adding their coefficients.
Term
 What is the Rule For Adding Algabraic Expressions with Like Terms?
Definition
 They can be combined by simply adding their coefficients. 3x+6x=9x
Term
 Factor: 9x+18
Definition
 3(x+6)
Term
 Factor: 4y²-12y
Definition
 4y(y-3)
Term
 Factor: (7x²+14x)/(2x+4)
Definition
 7x(x+2)/2(x+2) = 7x/2
Term
 If xᵃ = xᵇ, a and b are Integers, and x is a Positive Number Other Than 1, What Do You Know?
Definition
 a = bFor example, if you have 5ʸ = 125, you can determine that y=3, because 5³ = 125.
Term
 How Do You Multiply Two Algebraic Expressions?
Definition
 Multiply each term of the first expression by each term of the second expression.(4x+9)(x-5) = 4x(x) + 4x(-5) + 9(x) + 9(-5) = 4x² - 20x + 9x - 45 = 4x² - 11x - 45
Term
 Identity
Definition
 A statement of equality between two algebraic expressions which is true for all possible values of the variables.
Term
 Equation
Definition
 A statement of equality between two algebraic expressions that is true for only certain values of the variables.
Term
 Solution(s)
Definition
 The values of the variables which make a particular algebraic equation true.
Term
 Linear Equation
Definition
 An algebraic equation in which each term is either a constant, or the product of a constant and a variable, and where the variable is not raised to any power greater than 1.y = mx + b4x + 7 = -102x + 3y = 0
Term
Definition
 An algebraic equation which contains only one variable, where the variable is squared at least once.Written in the form: ax²+bx+c = 0Example: 4x²-20x-45 = 0
Term
 Base (in Relation to Powers)
Definition
 When an integer has an exponent, the integer is the base.In the expression 7², 7 is the base.
Term
 Exponent
Definition
 An integer which is used to indicate repeated multiplication of a number by itself.In the expression 7², 2 is the exponent.
Term
 Convert x⁻ᵃ to a Fraction, Assuming x is a Nonzero Real Number, and a is an Integers.
Definition
 1/xᵃ
Term
 Convert 1/xᵃ to a Base and Exponent, Assuming x is a Nonzero Real Number, and a is an Integers.
Definition
 x⁻ᵃ
Term
 Convert (xᵃ)(xᵇ) to a Single Base with Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 xᵃ⁺ᵇ
Term
 Convert xᵃ⁺ᵇ to an Algebraic Expression with Single-Variable Exponents, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 (xᵃ)(xᵇ)
Term
 Convert xᵃ/xᵇ to a Fraction Where the Numerator is 1, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 1/xᵇ⁻ᵃ
Term
 Convert xᵃ/xᵇ to a Single Base with Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 xᵃ⁻ᵇ
Term
 Convert 1/xᵇ⁻ᵃ to a Fraction with No Negative Numbers, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 xᵃ/xᵇ
Term
 Convert 1/xᵇ⁻ᵃ to a Single Base with Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 xᵃ⁻ᵇ
Term
 Convert xᵃ⁻ᵇ to a Fraction Where the Numerator is 1, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 1/xᵇ⁻ᵃ
Term
 Convert xᵃ⁻ᵇ to a Fraction with No Negative Numbers, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 xᵃ/xᵇ
Term
 What is the Value of x⁰, Assuming x is a Nonzero Real Number?
Definition
 1
Term
 What is the Value of 0⁰?
Definition
 Undefined.
Term
 Convert (xᵃ)(yᵃ) to a Single Base with Exponent, Assuming x and y are Nonzero Real Numbers, and a is an Integer.
Definition
 (xy)ᵃ
Term
 Convert (xy)ᵃ to an Algebraic Expression Where x and y are Both Bases, Assuming x and y are Nonzero Real Numbers, and a is an Integer.
Definition
 (xᵃ)(yᵃ)
Term
 Convert (x/y)ᵃ to a Simple Fraction, Assuming x and y are Nonzero Real Numbers, and a is an Integer.
Definition
 (xᵃ)/(yᵃ)
Term
 Convert (xᵃ)/(yᵃ) to an Algebraic Expression With a Single Exponent, Assuming x and y are Nonzero Real Numbers, and a is an Integer.
Definition
 (x/y)ᵃ
Term
 Convert (xᵃ)ᵇ to an Algebraic Expression with a Single Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 xᵃᵇ
Term
 Convert xᵃᵇ to an Algebraic Expression Where b is an Individual Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 (xᵃ)ᵇ
Term
 Convert xᵃᵇ to an Algebraic Expression Where a is an Individual Exponent, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 (xᵇ)ᵃ
Term
 Does (x + y)ᵃ = xᵃ + yᵃ?
Definition
 No. The expansion of (x + y)ᵃ should contain terms of the form 4xy.
Term
 When Using a Negative Sign in Front of the Base, Does it Matter Whether or Not There are Parenthesis?
Definition
 Yes!-x² is the negative of x², while and (-x)² is -x to the second power.
Term
 Solve: √(x²+y²)
Definition
 This cannot be done. While √(x²)=x and √(y²)=y, √(x²+y²) does NOT equal x+y.
Term
 Convert (a)/(x+y) to an Algebraic Expression Which Combines (Sums) Two Fractions, Assuming x is a Nonzero Real Number, and a and b are Integers.
Definition
 You can't do this. While (x+y)/a=(x/a)+(y/a), (a)/(x+y) does NOT equal (a/x)+(a/y)
Term
 What Does it Mean to "Solve an Equation"?
Definition
 To find the values of the variables that make the equation true.
Term
 What Does it Mean to "Satisfy an Equation"?
Definition
 To find the values of the variables that make the equation true.
Term
 Fill in the Blank: To ______ an Equation, You Must Find the Values of the Variables that Make the Equation True.
Definition
 Satisfy (or Solve).
Term
 Equivalent Equations
Definition
 Two (or more) equations with the same solution.x+2=4 and 2x+8=12 are equivalent equations, because they are both only true when x=2.
Term
 What Happens When the Same Constant is Added or Subtracted from Both Sides of an Equation?
Definition
 The equality is preserved: the new equation is equivalent to the original equation.
Term
 If You Subtract 3 From One Side of an Equation, How Do You Ensure the New Equation is Equivalent to the Original?
Definition
 Subtract 3 from the other side.
Term
 If You Add 3 to One Side of an Equation, How Do You Ensure the New Equation is Equivalent to the Original?
Definition
 Add 3 to the other side.
Term
 What Happens When Both Sides of an Equation are Multiplied or Divided by the Same Nonzero Constant?
Definition
 The equality is preserved: the new equation is equivalent to the original equation.
Term
 If You Multiply One Side of an Equation by 3, How Do You Ensure the New Equation is Equivalent to the Original?
Definition
 Multiply the other side by 3.
Term
 If You Divide One Side of an Equation by 3, How Do You Ensure the New Equation is Equivalent to the Original?
Definition
 Divide the other side by 3.
Term
 Solve: 5x-2-x = 3(x-2)-2x
Definition
 5x-2-x = 3x-6-2x (factored)4x-2 = x-6 (like terms combined)4x-2+2 = x-6+2 (2 added to both sides)4x-x = x-4-x (x subtracted from both sides)3x = -43x/3 = -4/3 (both sides divided by 3)x = -4/3 OR -1.33333...
Term
 How Do You Solve Linear Equations in One Variable?
Definition
 Simplify each side of the equation by combining like terms. Then use the rules for producing simpler equivalent equations.
Term
 What is One Way to Check Your Solution to a Linear Equation in One Variable?
Definition
 Substitute your solution into the original equation.
Term
 What is the Minimum Number of Solutions a Linear Equation Can Have?
Definition
 Zero. Some linear equations do not have solutions.
Term
 Ordered Pair
Definition
 The solution to an equation with two variables.Written like this: (x,y).
Term
 How Many Solutions Does a Linear Equation with Two Variables Have?
Definition
 Infinitely many.
Term
 How Do You Find the Solution to a Linear Equation with Two Variables?
Definition
 You can do this if you have another linear equation with the same variables.You would use either substitution or elimination.
Term
 System of Variables
Definition
 Two equations with the same variables.
Term
 Simultaneous Equations
Definition
 The equations in a sytem of variables.
Term
 Substitution
Definition
 One equation is manipulated to express one variable in terms of the other. Then the expression is substituted into the other equation.
Term
 Using Substitution, Solve This System: 2x-3y=-2 and 4x+y=24
Definition
 4x+y = 244x+y-4x = 24-4x (subtract 4x from each side)y = -4x+242x-3(-4x+24) = -2 (substitute the solution for y into the other equation)2x+12x-72 = -2 (factor)2x+12x-72+72 = -2+72 (add 72 to both sides)14x/14 = 70/14 (divide both sides by 14)x=5y = -4(5)+24 = -20+24 = 4 (substitute the value for x into the solution for y)Solution: (5,4)
Term
 Elimination
Definition
 Make the coefficients of one variable the same in both equations. Eliminate that variable using addition or subtraction.
Term
 Using Elimination, Solve This System: 4x-3y=25 and -3x+8y=10
Definition
 Multiply to get the same coefficient for one variable: 3(4x-3y=25) and 4(-3x+8y=10)Factor both sides: 12x-9y=75 and -12x+32y=40Add them together to get: 23y=115Divide by 23: y=5Substitute y into one of the equations: 4x-3(5)=25Factor: 4x-15=25Add 15 to both sides: 4x=40Divide both sides by 4: x=10Solution: (10,5)
Term
 How Many Solutions Does a Quadratic Equation Have?
Definition
 Zero, one, or two.
Term
 How Do You Solve a Quadratic Equation?
Definition
 Use the quadratic formula. You can also factor in some cases.
Term
Definition
 It always works.
Term
Definition
 It is sometimes faster.
Term
Definition
 x = [-b +/- √(b²-4ac)]/2aThe notation +/- means you have to solve it twice: once for - and once for +.
Term
 Use the Quadratic Formula to Solve: x²-4x-8 = 0
Definition
 x = [-(-4) +/- √((-4)²-4(1)(-8))]/2(1)x = [4 +/- √(16+32)]/2x = (4 +/- √48)/2x = [4 +/- √(3)(16)]/2x = (4 +/- 4√3)/2x = [2(2 +/- 2√3)]/2x = 2 +/- 2√3x = 2+2√3 AND 2-2√3In decimal form: x = 5.464 AND -1.464
Term
 Use Factoring to Solve: x²+5x+6 = 0
Definition
 Factor: (x+2)(x+3) = 0Solve each Factor: x+2=0 and x+3=0x=-2 and x=-3Solution: -3,-2
Term
 Linear Inequality
Definition
 A mathematical statement that uses one of the inequality signs:< > ≤ ≥ And where the variable is not raised by any power greater than 1.
Term
 Solve an Inequality
Definition
 To find the set of all values of the variables that make the inequality true.
Term
 Solution Set of an Inequality
Definition
 The set of all values of the variables that make the inequality true.
Term
 Equivalent Inequality
Definition
 Two qualities that have the same solution.
Term
 What Happens When the Same Constant is Added or Subtracted from Both Sides of an Inequality?
Definition
 The inequality is preserved: the new inequality is equivalent to the original inequality, and the direction of the inequality is preserved.
Term
 If You Subtract 3 From One Side of an Inequality, How Do You Ensure the New Inequality is Equivalent to the Original?
Definition
 Subtract 3 from the other side.
Term
 If You Add 3 to One Side of an Inequality, How Do You Ensure the New Inequality is Equivalent to the Original?
Definition
 Add 3 to the other side.
Term
 What Happens When Both Sides of an Equation are Multiplied or Divided by the Same Nonzero Constant?
Definition
 IF THE CONSTANT IS POSITIVE: The inequality is preserved: the new inequality is equivalent to the original inequality, and the direction of the inequality is preserved.IF THE CONSTANT IS NEGATIVE: The direction of the inequality must be reversed to preserve the inequality.
Term
 If You Multiply One Side of an Inequality by 3, How Do You Ensure the New Inequality is Equivalent to the Original?
Definition
 Multiply the other side by 3.
Term
 If You Divide One Side of an Inequality by 3, How Do You Ensure the New Inequality is Equivalent to the Original?
Definition
 Divide the other side by 3.
Term
 If You Multiply One Side of an Inequality by -3, How Do You Ensure the New Inequality is Equivalent to the Original?
Definition
 Multiply the other side by -3 AND reverse the direction of the inequality.
Term
 If You Divide One Side of an Inequality by -3, How Do You Ensure the New Inequality is Equivalent to the Original?
Definition
 Divide the other side by -3 AND reverse the direction of the inequality.
Term
 Solve: 2x ≤ 9
Definition
 2x/2 ≤ 9/2x ≤ 9/2x ≤ 4.5
Term
 Solve: x+3 < 0
Definition
 x+3-3 < 0-3x < -3
Term
 Solve: -2x < 5
Definition
 -2x/-2 > 5/-2x > -5/2x > -2.5NOTE THAT THE INEQUALITY IS REVERSED!
Term
 Function
Definition
 An algebraic expression which produces a single result for each value of the variable.Any input for a function produces a single output.They are usually denoted by the letters f, g, and h. For example: f(x) = 2x+6
Term
 Fill in the Blank: g(x) = 2x+6 is an Example of a ______.
Definition
 Function.
Term
 Domain
Definition
 The set of all permissible inputs of a function.Sometimes, the domain of a function is given explicitly and is restricted to specific values of x.
Term
 If the Domain of a Function is Not Explicitly Defined, What is the Domain?
Definition
 All values of x for which f(x) is a real number.
Term
 What Does it Mean if a Particular Variable Causes a Function to be Undefined?
Definition
 That variable is outside the range for the function.For example, if we plug 9 into the equation: 3x/x-9, we get 27/0, which is undefined. Therefore, the domain of this function is all real numbers except for 9.
Term
 Interest
Definition
 An amount added to the original amount, usually over time.
Term
 Simple Interest
Definition
 Interest which is based on the initial amount (called the principle) for the entire time period.
Term
 What is the Equation Used to Calculate Simple Interest?
Definition
 V = P[1+(rt/100)]Where V is the new value, P is the original value, r is the interest rate, and t is the time.
Term
 Compound Interest
Definition
 Interest which is added to the principle at regular time intervals, where interest is earned on the new amount.
Term
 What is the Equation Used to Calculate Compound Interest Which is Compounded Yearly?
Definition
 V = P(1+r/100)ᵗWhere V is the new value, P is the original value, r is the interest rate, and t is the time.
Term
 What is the Equation Used to Calculate Compound Interest With and Annual Interest Rate Which is Compounded More Than Once Per Year?
Definition
 V = P(1+r/100n)ⁿᵗWhere V is the new value, P is the original value, r is the interest rate, t is the time, and n is the number of times per year it is compounded.
Term
 If \$3000 is Invested At a Simple Interest Rate of 17%, What is the Value After 3 Years?
Definition
 V = \$3000[1+({17}{3}/100)]V = \$3000[1+(51/100)]V = \$3000(1+0.51)V = \$3000(1.51)V = \$4530
Term
 If \$3000 is Invested At a Compound Interest Annual Rate of 17% Which is Compounded Annually, What is the Value After 3 Years?
Definition
 V = \$3000(1+{17}/100)⁽³⁾V = \$3000[1+0.17]³V = \$3000(1.17)³V = \$3000(1.601613)V = \$4804.839Which is simplified to: \$4804.84
Term
 If \$3000 is Invested At a Compound Interest Annual Rate of 17% Which is Compounded Monthly, What is the Value After 3 Years?
Definition
 V = P(1+r/100)ᵗV = \$3000(1+{17}/100{12})⁽¹²⁾⁽³⁾V = \$3000(1+17/1200)³⁶V = \$3000[1+0.01416666666666666666666666666667]³⁶V = \$3000(1.01416666666666666666666666666667)³⁶V = \$3000(1.6593422013892234548898239271675)V = \$4978.0266041676703646694717815025Which is simplified to: \$4978.03
Term
 If the Value is \$4000 After 3 Years of Compound Interest with an Annual Rate of 17% Which is Compounded Monthly, What was the Original Investment?
Definition
 V = P(1+r/100n)ⁿᵗ\$4000 = P(1+{17}/100{12})⁽¹²⁾⁽³⁾\$4000 = P(1+17/1200)³⁶\$4000 = P[1+0.01416666666666666666666666666667]³⁶\$4000 = P(1.01416666666666666666666666666667)³⁶\$4000 = P(1.6593422013892234548898239271675)Now, we can solve it just like any other linear equation in a single variable:\$4000/(1.6593422013892234548898239271675) = P(1.6593422013892234548898239271675)/(1.6593422013892234548898239271675)2410.5937862914271522006019561891Which is simplified to: \$2410.59
Term
 If \$3000 is Invested for Using a Compound Interest Which is Compounded Monthly, and the Value After 3 Years is \$4000.26, What is the Annual Interest Rate?
Definition
 V = P(1+r/100n)ⁿᵗ\$4000.26 = \$3000(1+r/100{12})⁽¹²⁾⁽³⁾\$4000.26 = \$3000(1+r/1200)³⁶\$4000.26/\$3000 = (1200/1200+r/1200)³⁶1.33342 = (1200+r)/1200)³⁶1.33342 = (1200+r)³⁶/(1200)³⁶(1.33342)(1200)³⁶ = (1200+r)³⁶(1.33342)(\$7.08801)(10¹¹⁰) = (1200+r)³⁶(9.45131)(10¹¹⁰) = (1200+r)³⁶³⁶√[(9.45131)(10¹¹⁰)] = 1200+r1209.63000-1200 = r9.63000 = rWhich is simplified to: 9.63%
Term
 Rectangular Coordinate System
Definition
 Two real number lines that intersect at their respective zero points.
Term
 xy-Coordinate System
Definition
 Two real number lines that intersect at their respective zero points.
Term
 xy-Plane
Definition
 Two real number lines that intersect at their respective zero points.
Term
 What is it Called when Two Real Number Lines Intersect at Their Respective Zero Points.
Definition
 It can be called the rectangular coordinate system, the xy-coordinate system, or the xy-plane.
Term
 x-Axis
Definition
 The horizontal number line in a rectangular coordinate system.
Term
 y-Axis
Definition
 The verical number line in a rectangular coordinate system.
Term
 Origin
Definition
 The point where the x-axis and y-axis intersect in a rectangular coordinate system.
Term
Definition
 Any one of the four regions created by the x-axis and y-axis in a rectangular coordinate system.
Term
Definition
 The top right of the rectangular coordinate system.Note that both x and y are positive in this quadrant.
Term
Definition
 The top left of the rectangular coordinate system.Note that x is negative and y is positive in this quadrant.
Term
Definition
 The bottom left of the rectangular coordinate system.Note that both x and y are negative in this quadrant.
Term
Definition
 The bottom right of the rectangular coordinate system.Note that x is positive and y is negative in this quadrant.
Term
 Ordered Pair
Definition
 A point on the xy-plane, written as: (x,y)
Term
 x-Coordinate
Definition
 The first number in an ordered pair, indicating where along the x-axis the point is located.
Term
 y-Coordinate
Definition
 The second number in an ordered pair, indicating where along the y-axis the point is located.
Term
 What Are the Coordinates for the Origin?
Definition
 (0,0)
Term
 If a Point, P, Has the Coordinates (4,2) and Another Point, Q, Has the Coordinates (4,-2), What is Their Geometric Relation?
Definition
 Q is a reflection of P about the x-axis.OR: P and Q are symmetric about the x-axis.
Term
 If a Point, P, Has the Coordinates (4,2) and Another Point, Q, Has the Coordinates (-4,2), What is Their Geometric Relation?
Definition
 Q is a reflection of P about the y-axis.OR: P and Q are symmetric about the y-axis.
Term
 If a Point, P, Has the Coordinates (4,2) and Another Point, Q, Has the Coordinates (-4,-2), What is Their Geometric Relation?
Definition
 Q is a reflection of P about the origin.OR: P and Q are symmetric about the origin.
Term
 How Do You Find the Distance Between Two Points on the xy-Plane?
Definition
 Use the Pythagoream theorem.a²+b² = c²
Term
 What is the Pythagorean theorem?
Definition
 The equation used to obtain a diagonal when the distance along the x-plane and the distance along the y-plane are both known.a²+b² = c²
Term
 If P is at (4,3) and Q is at (-4,-3), What is the Distance Between Them?
Definition
 Distance on the x-plane: (4)-(-4) = 4+4 = 8Distance on the y-plane: (3)-(-3) = 3+3 = 6Diagonal: (8)²+(6)² = c²c² = 64+36c² = 100c = √100c = 10The distance between them is 10.
Term
 How Do You Represent an Equation in Two Variables on the xy-Plane?
Definition
 Graph the equation by finding the set of all points whose ordered pairs satisfy the equation.
Term
 Graph of an Equation
Definition
 The set of all points whose ordered pairs satisfy an equation in two variables.
Term
 Slope
Definition
 The ratio of two points along the graph of an equation, of the form (y₂-y₁)/(x₂-x₁).This is often referred to as the rise over the run. Note that it does not matter which point is defined as (x₁,y₁) and which is defined as (x₂,y₂).
Term
 What is the Slope of a Linear Equation with the Form y=mx+b?
Definition
 The slope is m.
Term
 x-Intercept
Definition
 The x-coordinates of the point(s) where the graph intersects with the x-axis.y=0 at this point.
Term
 y-Intercept
Definition
 The y-coordinates of the point(s) where the graph intersects with the y-axis.x=0 at this point.
Term
 If the x-Intercept is 6, What is the Value of y at This Location?
Definition
 The value of y is 0.The value of y is always 0 at the x-intercept.
Term
 If the y-Intercept is -3, What is the Value of x at This Location?
Definition
 The value of x is 0.The value of x is always 0 at the y-intercept.
Term
 What is the y-Intercept of a Linear Equation with the Form y=mx+b?
Definition
 The y-intercept is b.
Term
 When Describing the Slope, Which Value is the Rise?
Definition
 The change in y when moving from the first point to the second; (y₂-y₁).This is the numerator of the slope ratio.
Term
 When Describing the Slope, Which Value is the Run?
Definition
 The change in x when moving from the first point to the second; (x₂-x₁).This is the denominator of the slope ratio.
Term
 What is the Slope of a Vertical Line?
Definition
 Undefined.
Term
 What is the Slope of a Horizontal Line?
Definition
 0
Term
 What is the Form of the Equation for a Vertical Line?
Definition
 x = a, where a is the x-intercept.
Term
 What is the Form of the Equation for a Horizontal Line?
Definition
 y = b, where b is the y-intercept.
Term
 Parallel
Definition
 When two lines have the same slope, they are considered parallel.This means they can continue forever without touching.
Term
 Reciprocal
Definition
 The inverse of a fraction, so that the numerator becomes the denominator, and the denominator becomes the numeratorThe reciprocal of 3/5 is 5/3.
Term
 Negative Reciprocal
Definition
 The inverse of a fraction with the opposite sign, so that the numerator becomes the denominator, and the negative of the denominator becomes the numeratorThe negative reciprocal of 3/5 is -5/3.
Term
 Perpendicular
Definition
 When the slopes of two lines are negative reciprocals of one another.They will intersect one another at a 90-degree angle.
Term
 What is the Slope of a Line Passing Through Points P(3,-5) and Q(-2,-1)?
Definition
 [(-1)-(-5)]/[(-2)-(3)](-1+5)/(-2-3)4/-5-4/5
Term
 If the Slope of a Line is 3 and One of the Points is (6,2), What is the y-Intercept?
Definition
 y = 3x+b2 = 3(6)+b2 = 18+b-16 = bThe y-intercept will be -16.
Term
 How Do You Use the Graph of a System of Linear Equations in Two Variables to Illustrate Its Solution?
Definition
 Solve each equation for y in terms of x, then graph both equations.The intersection will be the solution.
Term
 How Do You Use the Graph of a System of Linear Inequalities in Two Variables to Illustrate Its Solution?
Definition
 Solve each equation for y in terms of x, graph both equations, then shade the appropriate side of the line.If y is less than the x solution, the graph of the equation consists of the region below that line.If y is more than the x solution, the graph of the equation consists of the region above that line.If y is less than or equal to the x solution, the graph of the equation consists of the line AND the region below that line.If y is more than or equal to the x solution, the graph of the equation consists of the line AND the region above that line.The intersection of the two regions (all points where both graphs meet) is shaded.
Term
 What is Special About a Line with Equation y=x?
Definition
 1) It will pass through the origin.2) It will have a slope of 1.3) It will make a 45-degree angle with each axis.4) For any point with coordinates (a,b), the point with interchanged coordinates (b,a) will be a reflection of (a,b) about the line y=x.To put it another way, (a,b) and (b,a) are symmetric about the line y=x.
Term
 What Happens if You Interchange x and y in the Equation of Any Graph?
Definition
 It yields another graph that is the reflection of the original graph about the line y=x.
Term
 Line of Symmetry
Definition
 The line around which the two lines are reflected.
Term
 What is the Line of Symmetry for the Graphs of an Equation and the Interchange of that Equation?
Definition
 y=x
Term
 Parabola
Definition
 The graph of a quadratic equation of the form y = ax²+bx+c, where a, b, and c are constants, and a is a nonzero real number.
Term
 Vertex
Definition
 The point of the graph of a quadratic equation that lies on the line of symmetry.
Term
 If the Vertex of a Quadratic Equation of the Form y = ax²+bx+c is its Lowest Point, What Do You Know About a?
Definition
 You know that a is positive.
Term
 If the Vertex of a Quadratic Equation of the Form y = ax²+bx+c is its Highest Point, What Do You Know About a?
Definition
 You know that a is negative.
Term
 What Are the x-Intercepts of a Parabola?
Definition
 The solutions of the equation ax²+bx+c = 0.
Term
 What Are the x-Intercepts of an Equation of the Form y = ax²+bx+c?
Definition
 The solutions of the equation ax²+bx+c = 0.
Term
 When Graphing a Function, Which Axis Do You Use for the Input?
Definition
 The x-axis.
Term
 When Graphing a Function, Which Axis Do You Use for the Output?
Definition
 The y-axis.
Term
 Fill in the Blank: Every Parabola is ______ with Itself About the Vertical Line that Passes Through its Vertex.
Definition
 Symmetric.
Term
 Fill in the Blank: Every Parabola is symmetric with Itself About the Vertical Line that Passes Through its ______.
Definition
 Vertex.
Term
 Fill in the Blank: The Two x-Intercepts of a Parabola are ______ from the Line of Symmetry.
Definition
 Equidistant.
Term
 Fill in the Blank: The Two x-Intercepts of a Parabola are Equidistant from the ______.
Definition
 Line of symmetry.
Term
 What is the Graph of an Equation of the Form r² = (x-a)²+(y-b)²?
Definition
 A circle with its center at the point (a,b) and a radius of r.
Term
 Describe the Graph of this Equation: 100 = x²+y²
Definition
 A circle with its center at the origin and a radius of 10.
Term
 Describe the Graph of this Equation: (x-6)²+(y+5)² = 9
Definition
 A circle with its center at (6,5) and a radius of 3.
Term
 How Do You Graph a Function?
Definition
 Represent each input, x, and its corresponding output, f(x), as a point (x,y) where y = f(x).
Term
 Piecewise-Defined Function
Definition
 A function which is defined by multiple subfunctions, each of which applies to a certain interval of the function's domain.Absolute value functions are examples of piecewise-defined functions.
Term
 What is the Shape of the Graph of an Absolute Value Function?
Definition
 It is v-shaped, with two linear pieces.
Term
 If f(x) = |x|+c, What is the y-Intercept?
Definition
 c
Term
 When Comparing the Graphs of f(x)=|x| and g(x)=|x|+c, What is Their Relationship?
Definition
 The graph of g(x) is shifted upwards from f(x) by c units.
Term
 When Comparing the Graphs of f(x)=|x| and g(x)=|x|-c, What is Their Relationship?
Definition
 The graph of g(x) is shifted downwards from f(x) by c units.
Term
 When Comparing the Graphs of f(x)=|x| and g(x)=|(x+c)|, What is Their Relationship?
Definition
 The graph of g(x) is shifted to the left of f(x) by c units.
Term
 When Comparing the Graphs of f(x)=|x| and g(x)=|(x-c)|, What is Their Relationship?
Definition
 The graph of g(x) is shifted to the right of f(x) by c units.
Term
 When Comparing the Graphs of f(x)=|x| and g(x)=c|(x)|, What is Their Relationship if c is More than One?
Definition
 The graph of g(x) is streched vertically versus f(x) by a factor of c.
Term
 When Comparing the Graphs of f(x)=|x| and g(x)=|(x-c)|, What is Their Relationship if c is More than Zero But Less than One?
Definition
 The graph of g(x) is shrunk vertically versus f(x) by a factor of c.
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