Algebra 2 Formulas and Vocabulary

Algebra 2 Formulas and Vocabulary

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Conjugate

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Cards (142)

Section 1

(50 cards)

Conjugate

Front

Used to rationalize the denominator of a fraction.

Back

Properties of Quadratics in Standard Form

Front

-The vertex is (-b/2a , f(-b/2a)) -The axis of symmetry is x=-b/2a -The y-intercept is C -If a > 0, the parabola opens up -If a < 0, the parabola opens down -If |a| > 1, the parabola is thinner than the parent -If |a| < 1, the parabola is wider than the parent

Back

Rate of Change

Front

Slope that represents how much one quantity changes on average, relative to the change in another quantity.

Back

GCF

Front

Greatest Common Factor

Back

Properties of 'i'

Front

-'i'='i' -'i^2'=-1 -'i^3'='-i' -'i^4'=1 -'i^5'='i' -'i^6'=-1 -'i^15'=-1 -'i^34'=-1

Back

Function

Front

A relation for which each input has exactly one output.

Back

Vertical Line Test

Front

A relation is a function if and only if no vertical line intersects the graph of the relation at more than one point.

Back

Expression

Front

A finite combination of symbols that are well-formed according to applicable rules.

Back

Properties of Quadratics in Vertex Form

Front

-The vertex is (h,k) -The axis of symmetry is x=h -If a > 0, the parabola opens up -If a < 0, the parabola opens down -If |a| > 1, the parabola is thinner than the parent -If |a| < 1, the parabola is wider than the parent

Back

Parallel Lines

Front

Lines are parallel if and only if they have the same slope.

Back

>

Front

Greater Than

Back

Elimination

Front

Back

Range

Front

Set of all output values.

Back

Simple Interest Formula

Front

I=Prt -P=principal (original amount of money) -r=interest rate (written as a decimal) -t=time (years)

Back

Parent Function

Front

The most basic function in a family.

Back

General Equation of an Absolute Value Function

Front

y=a|x-h|+k -a=rate of change -(h,k)=vertex

Back

Difference of Squares

Front

Back

Relation

Front

A mapping, or pairing, of input values with output values.

Back

Domain

Front

Set of all input values.

Back

Vertex Form of Quadratic Functions

Front

y=a(x-h)^2 +k -a≠0 -the graph is a parabola -Parent Function is f(x)=x^2

Back

Slope

Front

Denoted by 'm,' of a non-vertical line is the ratio of the vertical change to the horizontal change.

Back

Point-Slope Form

Front

y − y1 = m(x − x1). -m=slope -(x1,y1)=a given point

Back

Piecewise Functions

Front

A function that is defined by more than one function.

Back

Pythagorean Theorem of Baseball

Front

W/T≈R^2/R^2+A^2 -W=wins -T=games played -R=runs scored -A=runs allowed

Back

Celcius to Fahrenheit Conversion Formula

Front

F=(9/5)C+32 -F=degrees (fahrenheit) -C=degrees (celsius)

Back

<

Front

Less Than

Back

Absolute Value Graphs

Front

Back

Parabola

Front

Back

Standard Form of Linear Equations

Front

A linear equation in the form 'Ax+By=C.'

Back

Constant

Front

A non-varying value.

Back

Zeroes

Front

Solutions (also see 'Root / X-Intercept / Zero')

Back

Slope-Intercept Form

Front

y=mx+b -m=slope -b=y-intercept

Back

Absolute Value

Front

The distance a number is from 0 on a number line. (Can never be negative.)

Back

Alternating Current Voltage Formula

Front

E=IZ

Back

Square Root

Front

A number, 'r,' is a square root of a number, 's,' if r^2=s. -3^2=9 and (-3)^2=9 so 3 and -3 are square roots of 9

Back

Function Notation

Front

y=f(x), the value of the function when x is a certain value.

Back

Imaginary Numbers

Front

A complex number that can be written as a real number multiplied by the imaginary unit 'i.'

Back

G.E.M.D.A.S

Front

Grouping, Exponents, Multiplication, Division, Addition, Subtraction

Back

LCM

Front

Least Common Multiple

Back

Radical

Front

Operator to the square root.

Back

Substitution

Front

Back

Coefficient

Front

A multiplicative factor in some term of a polynomial, a series, or any expression.

Back

Principal Square Root

Front

The positive square root.

Back

Variable

Front

A symbol that represents a quantity in a mathematical expression, as used in many sciences.

Back

Standard Form of Quadratic Functions

Front

y=ax^2 +bx+c -a≠0

Back

Term

Front

A component of a logical or mathematical expression.

Back

Zero Product Property

Front

If AB=0, then A=0 or B=0.

Back

Complex Numbers

Front

A number that can be expressed in the form 'a+bi,' where 'a' and 'b' are real numbers and 'i' is the imaginary unit, that satisfies the equation i^2=-1.

Back

Perpendicular Lines

Front

Lines are perpendicular if and only if they have negative reciprocal slopes.

Back

Radicand

Front

Expression under the radical.

Back

Section 2

(50 cards)

Properties of Logarithms

Front

-log(b) xy = log(b) x + log(b) y -log(b) x/y = log(b) x - log(b) y -log(b) x^y = ylog(b) x

Back

Radical Form to Rational Exponent Conversion

Front

∜81=81^¼ Even Roots: -a < 0: no real nth roots -a = 0: one real nth root (0) -a > 0: two real nth roots Odd Roots: one real nth root

Back

Completing the Square

Front

Back

Change-Of-Base Formula

Front

log(c) a = (log a) / (log c)

Back

Percent Decrease Model

Front

y=a(1 - r)^t -a=initial value -r=% increase (or decrease) -t=time

Back

End Behavior

Front

The behavior of the graph of f(x) as 'x' approaches positive infinity or negative infinity.

Back

Factoring by Grouping

Front

The process of factoring four terms by grouping them in pairs, factoring the GCF from each pair, and looking for a common binomial factor.

Back

Quadratic Formula

Front

Back

Common Logarithm

Front

log(10) x written as log x

Back

Power Function

Front

y=ax^b, where 'a' is a real number and b is a rational number.

Back

Inverse Relation

Front

An interchange of the input and output values of the original relation.

Back

Vertical Motion Quadratic Function

Front

h(t)=-16t^2+vt+s -h=height of object (feet) -t=time (seconds) -v=initial velocity of object (ft/sec) -s=initial height of object (feet)

Back

Exponential Growth Function

Front

An exponential function that 'grows' away from the asymptote as you move left to right. -b > 1

Back

Square Root Function

Front

f(x) = √x

Back

Rational Exponent Rules

Front

-a^m * a^n = a^m+n -(a^m)^n = a^mn -(ab)^m = a^m * b^m -a^-m = 1/a^m -a^m / a^n = a^m-n. -(a/b)^m = a^m / b^m -ax^m ± bx^m = (a ± b)x^m

Back

Extrema

Front

The collection of the largest and smallest values of a function.

Back

Asymptote

Front

An imaginary line that a graph approaches more and more closely.

Back

Periodic Compounding Interest Formula

Front

A=P(1+r/n)^nt -A=amount of money after 't' years -P=principal (original amount of money) -r=interest rate (written as a decimal) -n=number of times the interest is compounded (paid) per year

Back

f(x)=(√x) +k

Front

Translates square root function 'k' units vertically.

Back

Decibel Level Formula

Front

D(I) = 10log(I/10^-12) -D(I)=the decibel level as a function of I -I=intensity of the sound (watts per square meter) -10^-12=intensity of the quitest sound a human can hear

Back

Polynomial Graphs

Front

Back

Product Property of Radicals

Front

√ab = √a * √b

Back

Polynomial Function

Front

f(x)=ax^n +bx^n-1 +cx^n-2+...+dx+e -a=leading coefficient -n=degree

Back

e

Front

The base of the natural logarithm. Approximately equal to 2.718281828459, it is the figurative asymptote of the function (1+1/n)^n.

Back

Horizontal Line Test

Front

The inverse of a function 'f' is also a function if and only if no horizontal line intersects the graph of 'f' more than once.

Back

Quotient Property of Radicals

Front

√(a/b) = (√a) / (√b)

Back

Discriminant

Front

A function of a polynomial's coefficients, giving information about the nature of its roots. -If b^2-4ac > 0, the (2) roots are positive -If b^2-4ac < 0, the roots are negative and imaginary -If b^2-4ac = 0, the (1) root equals zero

Back

Factoring with Cube Patterns

Front

Back

Absolute (Global) Extrema

Front

The collection of the largest and smallest values on the entire domain of a function.

Back

Exponential Decay Function

Front

An exponential function that 'decays' towards the asymptote as you move left to right. -0 < b < 1

Back

Exponential Function

Front

y=a(b)^x, a function in which the variable is in the exponent. -a=initial value -b=growth/decay factor

Back

Logarithm

Front

The inverse operation to exponentiation. y = log(b) x if and only if b^y = x -b > 0 -b ≠ 1 -x > 0

Back

Root / X-Intercept / Zero

Front

Where a function crosses the x-axis.

Back

Composition of a Function

Front

h(x)=g(f(x)), the pointwise application of one function to the result of another to produce a third function.

Back

Continous Combounding Interest Formula

Front

A=Pe^rt -A=amount of money after 't' years -P=principal (original amount of money) -r=interest rate (written as a decimal)

Back

Annual Price of Gasoline Cubic Function

Front

c(t)=0.0007t^3 - 0.014t^2 + 0.08t + 0.96

Back

Factoring Polynomials in Quadratic Form

Front

It is sometimes necessary to factor out any factor that might be common to all terms first. The two terms in 5x^2 - 10, for example, both contain the factor '5'. This means that the expression can be rewritten as 5(x^2 - 2).

Back

Cubic Root Function

Front

f(x) = a(∛(x-h)) + k a: -if |a|gets bigger, then there is a vertical stretch -if |a| gets smaller, then there is a vertical shrink -if a is negative, then the graph flips h: -translates graph 'h' units horizontally k: -translates graph 'k' units vertically

Back

Two-Step Factoring

Front

First, factor out any GCF from the original problem, then factor normally.

Back

Simplest Form of Radicals

Front

No perfect nth powers as factors and any denominator has been rationalized.

Back

Synthetic Substitution

Front

Back

Relative (Local) Extrema

Front

The collection of the largest and smallest values of a function within a given range.

Back

Synthetic Division

Front

Back

Exponent Rules

Front

-a^m * a^n = a^m+n -a^m / a^n = a^m-n. (a≠0) -(a^m)^n = a^mn -(ab)^n = a^n * b^n -(a/b)^n = a^n / b^n -a^-n = 1/a^n -a^0 = 1. (a≠0)

Back

Polynomial Long Division

Front

Back

Percent Increase Model

Front

y=a(1 + r)^t -a=initial value -r=% increase (or decrease) -t=time

Back

Inverse Function

Front

When both the original relation and the inverse relation are functions. -Written as f^-1(x) ✩ NOT A NEGATIVE EXPONENT!

Back

f(x)=√(x-h)

Front

Translates square root function 'h' units horizontally.

Back

Logarithmic Functions

Front

Back

Natural Logarithm

Front

log(e) x written as ln x

Back

Section 3

(42 cards)

Finding Vertical Asymptotes of a Rational Function

Front

Set denominator equal to zero.

Back

Hyperbola

Front

An open curve formed by a plane that cuts the base of a right circular cone. The set of all points in the plane such that the absolute value of the difference of the distances from two given points in the plane, called foci, is constant.

Back

Standard Equation of a Vertical Ellipse

Front

Back

Standard Equation of a Horizontal Hyperbola

Front

Back

Standard Equation of a Circle

Front

(x-h)^2 + (y-k)^2 = r^2 -(h,k)=any given point on the circle -r=radius

Back

Focus

Front

A fixed point used with a directrix to define a parabola.

Back

Finding Horizontal Asymptotes of a Rational Function

Front

-If power on bottom is bigger, then set 'y' equal to zero -If power on top is bigger, there is no asymptote -If powers are the same, then asymptote is coefficients

Back

Transverse Axis

Front

The axis of symmetry of a hyperbola that contains the vertices, and segment that connects the two vertices of the hyperbola.

Back

Matrix

Front

A rectangular pattern of data with rows and columns.

Back

Encrypting (Encoding) Matrixes

Front

Original Numbers * Encoding Matrix = Encoded Numbers

Back

Center of a Hyperbola

Front

The point halfway between the vertices of a hyperbola, or the midpoint of the transverse axis of a hyperbola. The center of a hyperbola is the point where the asymptotes intersect.

Back

Transformational Form of a Parabola

Front

-(x-h)^2 = 4p(y-k), opens up or down with a vertex at (h,k). -(y-k)^2 = 4p(x-h), opens left or right with a vertex at (h,k).

Back

Conjugate Axis

Front

The line segment of length '2b' that is perpendicular to the transverse axis and has the center of the hyperbola at its midpoint.

Back

Vertex of a Parabola

Front

Back

Excluded Values

Front

Values that are left out. (Make the denominator zero.)

Back

Directrix

Front

A fixed line used to define a parabola. Every point on the parabola is equidistant from the directrix and a fixed point called the focus.

Back

Focus of an Ellipse

Front

One of the two points that can be used to define an ellipse. For every point on an ellipse, the distance from the point to one focus, plus the distance from the point to the other focus, is equal to some constant value. Another name for a focus is a focal point. The plural of focus is foci. 'c' units from the center. c^2=a^2 - b^2.

Back

Vertices of a Hyperbola

Front

The endpoints of the transverse axis of the hyperbola.

Back

Midpoint Formula

Front

Back

How To Multiply Matrices

Front

Back

Major Axis

Front

Line through the widest part of an ellipse. '2a' units long.

Back

Complex Fractions

Front

Back

Minor Axis

Front

The shorter axis of an ellipse and perpendicular bisector of the major axis with endpoints on the ellipse. '2b' units long.

Back

Vertex of an Ellipse

Front

The endpoints of the major axis of the ellipse. 'a' units from the center.

Back

Ellipse

Front

A regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.

Back

Distance Formula

Front

Back

Finding X-Intercepts

Front

Find 'x' when y=0

Back

Finding Y-Intercepts

Front

Find 'y' when x=0

Back

Axis of Symmetry

Front

Back

Circle

Front

The set of all points in a plane that are the same distance from a given point called the center.

Back

Matrix Dimension

Front

The dimenions of a matrix are read row by column.

Back

Focal Width

Front

The width of the parabola at the focus. The width is 4p.

Back

Co-Vertex of an Ellipse

Front

The endpoints of the minor axis of the ellipse. 'b' units from the center.

Back

Extraneous Solution

Front

A solution that emerges from the process of solving the problem but is not a valid solution to the original problem.

Back

Decrypting (Decoding) Matrixes

Front

Encoded Numbers * Inverse of Encoding Matrix = Original Numbers

Back

Newton's Law of Cooling

Front

T(t) = S + (T - S)e^-kt -T(t)=temperature of the object after time 't' -S=temperature of the surrounding environment -T=initial temperature of the object -k=a constant that changes depending on the material properties of the object -t=amount of time (minutes) that has passed since the object began cooling

Back

Properties of Equality

Front

-b^x = b^y if and only if x=y -log(b) x = log(b) y if and only if x=y (b > 0, b ≠ 1)

Back

Rational Functions

Front

y=(a/(x-h)) + k, a polynomial divided by a polynomial.

Back

p

Front

Distance between the vertex and the focus. Also, the distance between the vertex and the directrix.

Back

Foci of a Hyperbola

Front

The absolute value of the difference of the distances from the two given points in the plane. 'c' units from center. c^2=a^2 + b^2.

Back

Standard Equation of a Vertical Hyperbola

Front

Back

Standard Equation of a Horizontal Ellipse

Front

Back