53 terms

ECHS-MrsZTEACHER

Consistent System

A system of equations that has at least one solution. Coinciding or Intersecting lines

Inconsistent System

A system of equations that has no solutions.

Parallel lines

Parallel lines

Dependent System

A system of equations that has infinite solutions

Coinciding lines

Coinciding lines

Independent System

A system of equations that has only one solution.

Intersecting lines

Intersecting lines

Slope

The change in the y-coordinates divided by the change in the x-coordinates.

Slope-intercept Form

y = mx + b

Point-slope Form

y- y₁ = m ( x - x₁)

Vertical line test

Used to determine if a relation is a function

Conjunction

an "AND" statement symbolized with a ∧

Disjunction

an "OR" statement symbolized with a ∨

Conditional

an "IF - Then" statement symbolized with a →

Bi-conditional

an "If and only if" statement symbolized with a ↔

Associative property

Shifting parenthesis only - do not change the order of the terms or factors

Commutative property

Change the order of the terms or factors

Distributive Property

Remove parenthesis by multiplying all terms by GCF or factor out the GCF and put in parenthesis

Transitive property

If a=b and b= c then a = c

Domain

the input values of a function. x-coordinates. independent variable

Range

the output values of a function. y-coordinates. dependent variable

Extraneous root

a solution which does not satisfy the original equation but works for a derived or obtained equation from the original problem.

y = x²

Parent function for all quadratic functions whose graph is a parabola.

y = x

Parent function for all linear function whose graph is a line.

Difference of two squares

product of conjugates

Perfect Square Trinomial

A binomial squared

Types of Central tendency

Mean, Median, Mode

Types of Dispersion

Range, Variance, Standard Deviation

Horizontal line

y = # has a slope of zero

Vertical line

x = # has an undefined slope

Ax + By = C

Standard form of a linear equation

Ax² + Bx + C = 0

Standard form of a quadratic equation

Vertex

The minimum or maximum point of a quadratic function which is at the point (h, k)

f(x) = a (x - h)² + k

Vertex form of a quadratic function The a determines whether the graph opens up or down and whether the graph is stretched, compressed or neither from the parent function. Vertex is at the point (h, k) Axis of symmetry is at x = h.

Radical expression

An expression with the independent variable in a radicand

Rational expression

An expression which is a quotient of two polynomials.

Coefficient

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression

Constant

A number without a variable as a factor

LCM

Least common Multiple - used to simplify complex fractions

LCD

Least common denominator - needed to add or subtract rational expressions

GCF

Greatest Common Factor -used to factor a polynomial

GCD

Greatest Common Divisor - used to reduce a rational expression

Excluded values

values of the variable at which a function is undefined

Multiplicative inverse of a matrix

a matrix, if it exists, such that the product of it and another matrix forms an identity matrix.

Mutually Exclusive

Two events that have no outcomes in common

Zero Product Property

If ab = 0 then either a = 0 and/or b = 0

Solution of an Equation

AKA Roots of the equation, zeroes of the function and x-intercepts

Lines with the same slope but different y-intercepts

Parallel lines

Lines with the same slope and y-intercepts

Coinciding lines

Lines with different slopes

Intersecting lines

Lines with different slopes which are opposite reciprocals

Perpendicular lines

Linear inequality

< or > the line is dashed ≤ or ≥ the line is solid < or ≤ shade below > or ≥ shade above You must solve for y before determining shading

Simplest radical form

a radical which contains no perfect roots

prime

a number which has only two factors one and itself

composite

a number which has more than two factors

Even root of an even power resulting in an odd exponent

you must put absolute value bars around the variable