Algebra 2 Vocab – Flashcards
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Reciprocal
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The product is 1. (Multiplicative inverse)
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Absolute value
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The distance of a number from zero on the number line.
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Extraneous solution
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A solution of an equation derived from an original equation that is not a solution of the original equation. Photo: The extraneous solution is crossed out
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natural numbers
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The set of numbers 1, 2, 3, 4, ... Also called counting numbers. (does not include zero)
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whole numbers
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Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
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integers
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All whole numbers (both positive and negative) and zero.
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rational numbers
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any number that can be expressed as a fraction Example: ¾
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irrational numbers
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numbers that cannot be expressed in the form a/b, where a and b are integers and b =0. Example: √2; 6.4367.....
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real numbers
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all numbers that are not imaginary (not √-1)
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compound inequalities
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two inequalities joined by the word "and" or the word "or"
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quadratic function
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A function that can be written in the standard form f(x) = ax² + bx + c where a ≠0. It's graph is a parabola
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Parabola
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The shape of the graph of a quadratic function.
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Axis of symmetry
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The line dividing a parabola into two parts.
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Vertex
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The point at which the parabola intersects the axis of symmetry. The y value of the vertex represents the maximum or minimum value of the function.
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vertex form of a quadratic function
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y = a(x - h )² + k, where (h,k) are the coordinates of the vertex of the function
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Factoring
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Rewriting an expression as the product of its factors. Example: Expanded form x² + x - 56 Factored form (x+8) (x - 7)
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Greatest common factor (GCF)
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The common factor with the greatest coefficient and the greatest exponent. Example: The GCF of 4x² +20 -12 is 4
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Difference of two sqaures
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An expression of the form a² - b².
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Zero product property
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If ab = 0, then a = 0 or b = 0 or both.
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Zero of a function
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A solution of an equation that equals zero.
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Imaginary numbers
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Any number of the form a + bi, where b ≠ 0 and i = √-1 Example: 2 + 3i
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Complex numbers
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Imaginary numbers and real numbers together make up the set of these numbers.
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Completing the square
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The process of finding the last term of a perfect square trinomial.
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Discriminant
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Part of the quadratic formula that equals the square root of b² - 4ac. Its value determines the number of real roots the equation has. If b² - 4ac 0, the equation has two real roots
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x intercept
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x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero
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y intercept
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the y-coordinate of the point where the graph crosses the y-axis
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perfect square trinomial (tri = 3, nom = name OR equation with 3 terms)
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the product you obtain when you square a binomial (2 terms)
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quadratic term
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in the equation f(x)=ax²+bx+c, it is ax²
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linear term
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in the equation f(x)=ax²+bx+c, it is bx
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constant term
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a term that has a number but no variable. in the equation f(x)=ax²+bx+c, it is c
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standard form of a quadratic equation
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y = ax² + bx + c
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Growth factor
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An exponential function where b is greater than one
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Decay factor
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An exponential function where b is greater than zero but less than one.
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asymptote
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A line that a graph approaches as x or y increases in absolute value
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Logarithm
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The inverse of an exponent
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Common logarithim
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A logarithim of base ten.
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Exponential equation
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An equation where the unknown is in the variable. Solve it by taking the logarithm of each side of the equation
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Logarithmic equation
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An equation where the unknown is in the logarithim.
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natural logarithm
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a logarithm with base e, written as ln
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exponential growth
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Growth at a constant rate of increase per unit of time; can be expressed as a constant fraction or exponent
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exponential decay
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a decrease that follows an exponential function
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change of base formula
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Used to evaluate a logarithm with any base (converts from one base to another)
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compound interest
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Interest earned on both the principal amount and any interest already earned.
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system of equations
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a set of two or more equations using the same variable
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linear system
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a set of two or more linear equations that use the same variable
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independent system
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a system of linear equations that has a unique solution
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dependent system
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a system of equations that does not have a unique solution
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equivalent systems
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linear systems that have the same solution
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constraints
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restrictions on the variables of the objective function in a linear programming problem
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coordinate space
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a three-dimensional space where each point is described uniquely using an ordered triple of numbers
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ordered triples
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(x,y,z)
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Absolute Value Function
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a function written in the form y = /x/, and the graph is always in the shape of a v
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Constant of Variation
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the number k in equations of the form y=kx
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Dependent Variable
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a factor that can change in an experiment in response to changes in the independent variable
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Direct Variation
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y=kx
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Domain
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The set of x-coordinates of the set of points on a graph; the set of x-coordinates of a given set of ordered pairs. The value that is the input in a function or relation.
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Function
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A relation which one element from the domain is paired with range
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Independent Variable
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variable that is changed in an experiment
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Linear Equation
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an equation whose graph is a straight line
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Linear Function
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a function in which the graph of the solutions forms a line
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Linear Inequality
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an inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line
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Parent Function
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The simplest function in a family; all functions in the family are transformations of it
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Point slope form
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y - y1=m(x - x1)
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Range
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The y-coordinates of the set of points on a graph. Also, the y-coordinates of a given set of ordered pairs.
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Reflection
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A transformation that "flips" a figure over a mirror or reflection line.
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Relation
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A set of ordered pairs
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Scatter Plot
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a graph with points plotted to show a possible relationship between two sets of data.
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Slope
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the steepness of a line, equal to the ratio of a vertical change to the corresponding horizontal change
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Slope Intercept Form
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the equation of a line in the form of y= mx + b, where m is the slope and b is the y intercept
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Standard Form (Linear)
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ax + by = c
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Transformation
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An operation that moves or changes a geometric figure in some way to produce a new figure
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Translation
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A transformation that "slides" each point of a figure the same distance in the same direction.
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Trend Line
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a line that approximates the relationship between the data sets of a scatter plot
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Vertex
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The point in a function where the function reaches a min or a max
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Vertical Line Test
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a method to determine if a graph is a function or not
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x-intercept
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The x-coordinate of the point where a line crosses the x-axis.
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y-intercept
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the y-coordinate of the point where the line crosses the y-axis.
