Algebra Final Review Stack

distance

rate x time

infinate solutions

lines are the same

all real numbers

inequality true

no solution

lines are parallel, solutions are not true

intrest

part x rate x time

open circle

less than, greater than, dashed line

closed circle

less than or equal to, greater than or equal to, solid line

and inequalities

both inequalities must be satisfied on number line

or inequalities

only 1 inequality needs to be satisfied

absolute value

The distance of a number from zero on a number line. In an expression, numbers cannot be distributed, and it cannot equal a a negative number before evaluating

slope-intercept form

y = mx + b

horizontal line

0

verticle line

undefined

point-slope form

y - y₁ = m(x - x₁)

standard form

Ax+By=C

parallel lines

Lines that never intercect. They have the same slope, yet different y-intercepts

perpendicular lines

Lines that incerept to form right angles. Their slopes are opposite recipricols, and they have different y-intercepts

relation

a set of ordered pairs

function

each input has exactly one output

x

independant

y

dependant

continuous function

includes all real numbers

discrete function

just the whole numbers of integers

one to one function

every input has exactly one output

parent function

function we start with before transformations, f(x)=x

verticle translation

f(x)=x+k

k>0

verticle shift up

k<0

verticle shift down

horizontal translation

f(x)=(x-h) , h is not true to its sign

h>0

horizontal shift right

h<0

horizontal shift left

transformation form

f(x)=(x-h)+k

sequence

an ordered list of numbers that forms a pattern

arethmatic sequence

has a common difference between each term in sequence

recursive formula

a1=___; an = an-1 + d

explicit formula

an = a + (n - 1)d

no association

refers to the absence of a relationship between two variables. If there is no connection between the variables, the value of one variable does not affect the value of the other.

strong correlation

A relationship between two variables where a change in one is consistently associated with a change in the other. This suggests a high level of association and accurate prediction between the two variables.

weak correlations

Weak correlation means little to no relationship between two variables. Changes in one variable do not significantly impact the other variable. Weak correlations are shown by a correlation coefficient close to zero.

line of best fit

trend line that matches the data/points the greatest

correlation coefficent

a statistical measure that quantifies the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

bivariate data set

data set with 2 variables

residual

difference between the y-value and the corresponding y-value

interpolation

using a model to estimate a value within the range of known values

extrapolation

using a model to make a prediction about a vaule outside of known values

causation

describes a cause and effect relationship

product of powers

quotient of powers

power of product

negative exponents

0 exponent

equal to 1

rational exponents

graphing exponential functions

f(x)=ab^x

exponential growth

f(x)= a(1+r)^x

compound interest

a=p(1+r/n)^nt

exponential decay

f(x)=a(1-r)^x

geometric recursive formula

an=(an-1)(r)

geometric explicit formula

an=(a1)(r^n-1)

transformin exponential functions

f(x)=a^(x-h)+k

polynomial

a monomial or the sum or difference of two or more monomials called terms

degree of polynomials

the total of exponents per term

Suppose we have a polynomial with the terms 3x^4 - 2x^2 + 5. The degree of this polynomial is 4, since the highest power of x is 4.

finding vertex

(-b/2a,f(-b/2a))

standard form

f(x)=ax^2+bx+c

multiplying radical expressions

multiply whats in and out of radical expressions

Suppose we want to find the product of √2 and √3. We can simplify this expression by multiplying the numbers inside the radicals: √2 × √3 = √(2×3) = √6. Therefore, the product of √2 and √3 is equal to √6.

imaginary numbers

Numbers that cannot be expressed as the product of a real number and the square root of a negative number. Symbolized by "i". Used in complex numbers.

completing a square

(b/2)^2

quadratic formula

x = (-b ± √(b² - 4ac)) / 2a

vertex form

f(x) = a(x-h)^2 + k

finding x intercepts

make Y 0

EXP: 0=2x^2+6x+5

finding y intercept

evauate x for 0

EXP: f(0)=2(0)^2+6(0)+5

f(0)=5