Algebra 2
Finding the vertex formula
-(b/2a)
formula for the focus or directrix
1/4a
focus
1/4a above
directrix
1/4a below
System of equations
2 or more that have 2 or more variables. A system of equations generally has one solution, which is an ordered pair with numbers that satisfy each of the equations
Exponential function
3*2^x=f(x)
Two-way frequency table
A chart used for listting the different ways that things can have or not have certain attributes
Unit circle
A circle with a radius of 1 and center at (0,0).
Finite arithmetic series formula
A formula S,n=(a,1+a,L)n/2 for summing the terms of a finite arithmetic series
Finite Geometric series formula
A formula S,n=a,1(1-r^n)/1-r for summing the terms of a finite geometric series.
Cubic function
A function of the f(x)=Cubic equation
Rational function
A function that has a fraction with a polynomial of degree at least one in the denominator.
Trigonometric function
A function that involves a trigonometry ratio, like sine, cosine, or tangent. f(x)=3 sin(x)+1 is a trigonometric function.
Odd function
A function whose graph is symmetric with respect to the origin.
Even function
A function whose graph is symmetric with respect to the y-axis.
Linear function
A function whose largest exponent is 1. f(x)=3x+7 is a linear function
Quadratic function
A function whose largest exponent is 2 f(x)=x^2-3x+7 is a quadratic function
Variable
A letter that is used to represent a number. Often this letter represents the thing to be solved for in an equation. In the expression 2x+5, the variable is x
Asymptote
A line that a curb gets closer and closer to with out ever reaching
e
A mathematical constant that is involved in many questions related to modeling growth. It is approximately 2.72.
Complex number
A number of the form a+bi where a and b are real numbers. 5+3i is a complex number.
Imaginary number
A number that is a multiple of the imaginery unit i. 5i is an imaginery number.
constant
A number; the term is a poolynomial that has no variable part. in the polynomial 2x+3, the x constant is 3
Perfect square trinimoial
A polynomial of the form x^2+2ax +a^2 or x^2-2ax+a^2 that can be factored into (x+a)^(2) or (x-a)^(2). For example, x^(2)+6x+9 can be factored into (x+3)^(2)
Monomial
A polynomial that has just one term. The Polynomial 3x^(5) is a monomial
Trinomial
A polynomial with three terms
Binomial
A polynomial with two terms. The expression 2x+5 is a binomial
Survey
A question or set of questions designed to collect data about a specific group of people, or population.
Function
A rule that takes a number or expression as an input and converts it into a number or expression in a predictable way. The function f(x)=x^2 takes a number or expression squared. for example, f(3)=3^2=9
Geometric sequence
A sequence of numbers like 3, 6, 12, 24..., where each number is equal to the previous number in the sequence multiplied by the same number. That number, the common ratio, is called r. In this case, r=2.
ln x
A shorthand for writing log of e x.
i
A shorthand way of writing sqrt(-1)
Factor theorem
A theorem that states that if the remainder when you divide P(x) by x-a is 0, then x-a is a factor of P(x).
Degree
A unit of angel measurement that is 1/360 of a circle.
Radian
A unit of angle measurement that is equal to approximately 57 degrees.
Explicit sequence formula
A way of describing a sequence based on relating the position of a term to the number in that position. a,n=5n+8 is an explicit sequence formula.
Recursive sequence formula
A way of dscribing a sequence based on how each term relates to the preceding term. a,1=3, a,n=5+a,n-1 is a recursive sequence formula.
Difference of perfect squares
A way of factoring a polynomial like x^2-3^2 into (x-3)(x+3). In general, an expression of the for a^2-b^2 can be factored into (a-b)(a+b).
Factor by grouping
A way of factoring that involves separating a polynomial int two or more groups, finding a common factor in each group, and, if possible, factoring a common factor out of what remains. the expression. x^(3)+3x^(2)+2x+6=x^(2)(x+3)+2(x+3)=(x+3)(x^(2)+2)
Standard Deviation
A way of measuring how "spread out" a data set is. The smallest standard deviation is 0 when all the elements of a set are equal.
Venn Diagram
A way of organizing data that have two or more intersecting circles surrounded by a rectangle.
FOIL
A way to remeber the four multiplications when multipliying one binomial by another binomial. When multiplying (2x+3)(4x+5)
Radical Equation
An equation involving a radical expression. sqrt(x+2)=5 is a radical equation.
Cubic equation
An equation of the form ax^(3)+bx^(2)+cx+d=0
Quadratic equation
An equation of the form ax^2 +bx+c=0
Exponential equation
An equation that invloves an exponential expression. 3*2^x=96 is an exponential equation
Rational equation
An equation that involves one or more rational expressions 3/x-2 + 2/x-2=5
Logarithm
An exponent that tells what a base needs yo nr raised to in order to become another number. The Logarithm of 25 base 5= 2 since 5^(2)=25
Radical expression
An expression involving a radical symbol. sqrt(x+2) is a radical expression
Polynomial
An expression like 2x^(3)+5x^(2)-3x+7 that conssts of one or more terms, each term having a coefficient and a variable raised to a power.
Vertex form of a quadratic expression
An expression of the form y=a(x-h)^2+k. When graphed, it is a parabola with vertex (h,k).
Rational expression
An expression that has a fraction with a polynomial of degree at least one in the denominator.
Arithmetic series
Does some of the terms in and arithmetic sequence. 3+7+11+15 is an arithmetic series
Directrix
Every point on a parabola is equivalent from a point and a line. That is called the directrix
Focus
Every point ona parabola is equidistant from a point and line. That point is called the focus on the parabola.
Exponential expression
Expression that has a variable as an exponent 3*2^x
Factoring
Finding two things whose product is a given thing. 15=3*5 is a way of factoring 15.
Inverse function
If a function f(x) has an inverse, f^(-1)(x), then f^(-1)((f(x))=x
Substitution method
In a system of equations, when one of the variables is solved in terms of the others and then substituted into the other equation. For example, the system of equations
Growth rate
In an exponential expression a(1+r)^(x), the r is the growth rate. For exmple, in 100(1+0.07)^(x), the growth rate is 0.07.
Base
In an exponential expression the base is the number being raised to a power. In the expression 5×2^(x), 2Is the base. In a logarithmic expression, the base is the small subscript number after the word
Elimination method
Multiplying one or more equations in a system of equations by a constant and then adding the equations in a way that makes one of the variables "cancel out". The system x+2y=5and 3x-2y=7 becomes 4x=12 when the 2 equations are added together
Greatest Common Factor
Of all the common factors between 2 numbers or polynomials, the one that is the largest. For example the numbers 12 and 18 have common factors of 1, 2, 3, 6, so 6 is the greatest common factor between 12 and 18.
Population Mean
The Average of an entire population for some characteristic. for example, if out of 10000 people studied, their average height is 64 inches, 64 is the population mean
Sample Mean
The average of a sample that has some characteristics. For example, if out of 10000 people 100 people are randomly chosen and, of those 100 people their average height is 61 inches, then 61 inches is the sample mean for that sample.
Probability
The chance of something happening ranging from 0 to 1; impossible to certain
Amplitude
The distance between the middle of sign or cosine curve to the top of that sign or cosine curve. When the equation is y=a sin (Bx) + d or y= a cos(bx)+d, amplitude is a.
Quadratic formula
The formula (-b[+/-]sqrt(b^(2)-4ac))/(2a) used to find the solutions to quadratic equation
Degree
The highest exponent in a polynomial. Inx^3+5x^2+7x+2 the degree is 3
Period
The number of dergees in one cycle of a sine or cosine curve
Frequency
The number of sine or cosine curves that can fit into a 360 degree interval.
log of b x
The number of which b would have been raised to geta result of x. For example, log of 125 of base 5=3 since 5^(3)=125
Coefficient
The number that gets multiplied by a variable in mathematical expression. In the expression 5x^(2), the coefficient of the x^(2) term is 5.
Sample proportion
The percent of a sample that has some characteristic. for example, if out of 10000 people, 100 people are randomly chosen and of those 100 people, 38% are boys, then 0.38 is the sample portion.
Population Proportion
The percent of an entire population that has some characteristic. for example, if out of 10000 people studied, 52% are boys, 0.52 is the population proportion.
Sine
The ratio between the opposite side and hypotenuse of a right triangle. Also the y-coordinate of a point on the unit circle.
Tangent
The ratio between the opposite side and the adjacent side of a right triangle
Arithmetic sequence
The sequence of numbers like three, seven, 11, 15,..., Where each number is the same amount more or less than the previous number. That difference is called D. In this case, D = four
Geometric series
The sum of the terms in a geometric sequence. 3+6+12+24 is a geometric series.
Remainder theorem
The theorem that states that when you divide a polynomial P(x) by x-a, the remainder will always equal P(a). For example, if you divide the polynomial P(x)=x^(2)+5x+6 by x-3, you will get a remainder of P(3)=30.
Algebraic identity
To Xpressions usually involving polynomials that can be shown to be equal to each other
Trigonometric identity
Two expressions involving trigonometric ratios that can be shown to be equal to one another.
Randomization test
When a computer is used to stimulate an ideal experiment with the goal of seeing if something that already happened was likely to happen or not.
Factors
When a number of a polynomial is divided by a number or polynomial and there is no remainder, the divisor is a factor of the dividend. Since 15/3=5 remainder 0, 3 is a factor of 15
Experimental study
When a researcher has one group of subjects how the 2 groups react. An example is giving half of the subjects one type of medicine and the rest of them another type of medicine.
Normal Distribution
When a set of data points resembles a bell cure with 68% being within one standard deviation and 95% being within two standard deviations.
Observational study
When a statistical researcher collects data by studying the behavior of the subjects without interferring with their environment
Horizontal Shift
When all the points of a graph move right or left the same number of units.
Vertical Shift
When all the points of a graph move up or down the same number of units.
Given
When calculating the probability of B given A, the "given" means that the event A has already happened, which may or may not affect the probability that B will also happen
Statistical significance
When data from an experiment are randomly mixed together multiple times with the goal of seeing if a difference between 2 groups was likely to happen.
Compound interest
When money in a bank gets interest on a initial deposit and then later gets more interest based upon on the original deposit and on the interest already earned
Sampling distribution of the sample mean
When multiple groups of samples are taken from a larger population and the percent of some attribute of each sample group is calculated and graphed in a histogram.
composite function
When the expression that defines one function is put into another function. If f(x)=3x and g(x)=x^(2) then g(f(x))=(3x)^2
Simplified radical form
When the number inside a square root sign has no factors that are oerfect squares. The expression sqrt(18) is not in simplified radical form since 18=2*9. 3sqrt(2), which is equal to sqrt(18), is in simple radical form.
Dependent events
When the probability of ob event is affected by whether or not some other event happened, they are called dependent events.
Independent events
When the probability of one event is not affected by whether or not some other event happened. The event "I wake up at 700" and "It will rain today" are independent events
Horizontal shrink
When the x-coordinats of every point in a graph are divded by the same number.
Vertical stretch
When the y-coordinates of every point in a graph are multiplied by the same number
Like terms
When two monomials with the same variable part are added or subtracted. 2x^2 and 3x^2 are like terms
z-score
a measure of how many standard deviations you are away from the norm (average or mean)
Completing the Square Method
divide b by 2 and square it to find c, and then find the root
y intercept in any equation
is the last term or c
Cosine
ratio of the adjacent side to the hypotenuse of a right-angled triangle. Also the x-coordinate of a point on the unit circle
Sample Space
the set of all possible outcomes of a probability experiment
Standard dorm of a quadratic expression
y=ax^(2)+bx+c