53 terms

ECHS Algebra 2 Test 8

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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
Dependent System
A system of equations that has infinite solutions
Coinciding lines
Independent System
A system of equations that has only one solution.
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