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Algebra 2 Final Review
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Gravity
Terms in this set (147)
system of two linear equations
two variables x and y also called a linear system consists of two equations
ordered pair
(x,y), a point on a graph
exactly one solution
infinitely many solution
no solution graph
substitution method
elimination method
system of linear inequalities
answer to a system of linear inequalities
the area shaded by both graphs
system of three linear equations
a system consisting of three linear equations in three variables
ordered triple
(x,y,z)
Real numbers
All numbers
Irrational numbers
Numbers that cannot be written as fractions, go on forever
rational numbers
Any number that can be expressed as a fraction
Integers
Positive and negative whole numbers
Whole numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
opposite
switching of signs
power
exponent
exponent
power; 3^4 it is the 4
base
3^4; it is the 3
terms
the parts of an expression that are added together
variable
A letter used to represent one or more numbers
constant term
a term with no variables
Coefficient
The number in front of a variable
Equation
A mathematical sentence that contains an equals sign.
Linear equation
an equation whose graph is a line
Solution
answer
equivalent equations
equations that have the same solution
formula
is an equation that relates two or more quantities
linear inequality
can be formed by replacing the equal sign in a linear equation with an inequality symbol
compound inequality
Two or more inequalities joined together by "and" or "or"
equivalent inequalities
inequalities that have the same solution
absolute value
The distance a number is from zero on a number line
extraneous solution
false answer
Rational Function
A function that can be written as a polynomial divided by a polynomial.
If the exponent in the denominator is larger than the exponent in the numerator; m<n, then...
the line has a horizontal asymptote at y=0.
If the exponent in the numerator is larger than the exponent in the denominator; m>n, then...
the graph has no horizontal asymptote.
If the exponents values are equal in the numerator and denominator then, m=n, then....
then the line has a horizontal asymptote at y=a/b where a and b are the leading coefficients.
Simplified Form
the numerator and denominator have no common factors.
Reciprocal
The multiplicative inverse of a number
to add or subtract rational exponents
the denominators need to be the same.
Complex Fraction
is a fraction that contains a fraction in its numerator or denominator
cross multiplying
solve a rational equation when each side of the equation is a single rational expression.
rational function graph
Least common Denominator
The least common multiple of the denominators of two or more fractions.
Horizontal Asymptote
a horizontal line that the curve approaches but never reaches
Vertical Asymptote
A vertical line that a graph approaches but never reaches.
Domain
x-values, input
Range
y-values, output
Exponential Function
a function of the form f(x) = ab^x, where a and b are real numbers with a ≠ 0, b>0, and b ≠ 1
Exponential Growth Function
A function of the form y=ab^x, where b is greater than 1 and a is greater than zero
Growth Factor
the b value of a growth function, greater than 1
asymptote
is a line a graph approaches
Exponential Decay Function
y = ab^x if a > 0 and 0 < b < 1
Decay Factor
the b value of a decay function, between 0 and 1
Euler's Number
e
logarithm of y with base b
The expression y = logb x is a logarithmic function
common log
base 10 log
natural log
base e or ln
product property of logarithms
logb mn = logb m + logb n
Quotient Property of logarthims
logb (m/n) = logb m - logb n
Power Property of logarthims
logb m^n = nlogb m
Exponential Equations
equations in which variable expressions occur as exponents
Logarithmic Equations
equations that involve logarithms of variable expressions
index of a radical
the value of n in the radical ^n√a
radical sign
√
rational exponent
fraction exponent
cube root
An idea similar to that of a square root, except that the root must be cubed
inverse function
A relation formed by reversing x and y in a function.
cubic function
a polynomial function with the highest power being three
quadratic function
a function in which the greatest power of the variable is 2
composition of a function
f(g(x))
radical function
a function that contains a radical with a variable in its radicand
like radicals
radical expressions that have the same index and radicand
What is the index of 3^(5/3)
The index is 3
What are the shifts of the following y=2√(x-1)+3
up 3, right 1, and stretched by 2
What are the shifts of the following y=2√(x+3)-1
down 1, left 3, and stretched by 2
Product of Powers
a^m * a^n = a^m+n
Power of a power
(a^m)^n = a^mn
Power of a product
(ab)^m = a^m b^m
Negative exponent
a^-n = 1/a^n
Zero Exponent
a^0 = 1
Quotient of powers
a^m/a^n = a^m-n
Power of a Quotient
(a/b)^m= (a^m)/(b^m)
Polynomial
is a monomial or the sum of monomials
polynomial function
a function that is represented by a polynomial equation
Leading Coefficeint
number in front of the highest degree
Degree
largest expoenent
Constant term
term without a variable
standard form
degrees decrease going left to right
(a+b)(a-b)
a^2-b^2
(a+b)^2
a^2+2ab+b^2
(a-b)^2
a^2-2ab+b^2
(a+b)^3
a^3+3a^2b+3ab^2+b^3
(a-b)^3
a^3-3a^2b+3ab^2-b^3
polynomial witha degree of 0
constant
polynomial with a degree of 1
linear
polynomial with a degree of 2
quadratic
polynomial with a degree of 3
cubic
polynomial with a degree of 4
quartic
synthetic division
the shortcut for long division of polynomials when dividing divisors of the form x - k
Long division
Long dividing equations by binomials to find the roots
Quadratic Function
y=ax^2+bx+c
Parabola
Vertex
The turning point
Vertex Form
y=a(x-h)^2+k
Axis of Symmetry
divides the parabola into mirror images; passes though the vertex
Intercept Form
y=a(x-p)(x-q)
Monomial
one term
binomial
two terms
trinomial
3 terms
quadratic equation
ax^2+bx+c=0
roots, zeros, x-intercepts
Solutions to a quadratic equation
a^2-b^2
(a-b)(a+b)
a^2-2ab+b^2
(a-b)^2
square root
√a
Radical sign
√
radicand
conjugate
a+bi, a-bi
i
√-1
complex number
a+bi
imaginary number
i
complex plane
place to graph complex numbers
absolute value of a complex number
√a^2+b^2
completing the square
quadratic formula
discriminant
b^2-4ac
f(x)=|x|
A relation for which each input has exactly one output
Function
Relation
a mapping, or pairing, of input values with output values
Linear function
a function in the form y=mx+b
Function notation
f(x)=mx+b
slope
rate of change, rise over run
m=
(y2-y1)/(x2-x1)
Parallel lines
two lines who don't intersect; same slope
Perpendicular lines
Two lines who cross at 90 degrees, opposite reciprocal slope
Slope-Intercept Form
y-intercept
where the graph crosses the y-axis; x=0
x-intercept
where the graph crosses the x-axis; y=0
Standard Form
Ax+By=C
Horizontal Line
slope is 0
Vertical Line
Slope is undefined
point-slope form
positive correlation
Negative correlation
Best-fitting line
V-shaped Graph
Absolute value
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