Algebra Final Review Stack

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Algebra

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70 Terms

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distance
rate x time
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infinate solutions
lines are the same
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all real numbers
inequality true
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no solution
lines are parallel, solutions are not true
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intrest
part x rate x time
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open circle
less than, greater than, dashed line
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closed circle
less than or equal to, greater than or equal to, solid line
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and inequalities
both inequalities must be satisfied on number line
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or inequalities
only 1 inequality needs to be satisfied
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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
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slope-intercept form
y = mx + b
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horizontal line
0
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verticle line
undefined
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point-slope form
y - y₁ = m(x - x₁)
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standard form
Ax+By=C
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parallel lines
Lines that never intercect. They have the same slope, yet different y-intercepts
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perpendicular lines
Lines that incerept to form right angles. Their slopes are opposite recipricols, and they have different y-intercepts
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relation
a set of ordered pairs
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function
each input has exactly one output
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x
independant
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y
dependant
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continuous function
includes all real numbers
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discrete function
just the whole numbers of integers
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one to one function
every input has exactly one output
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parent function
function we start with before transformations, f(x)=x
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verticle translation
f(x)=x+k
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k>0
verticle shift up
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k
verticle shift down
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horizontal translation
f(x)=(x-h) , h is not true to its sign
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h>0
horizontal shift right
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h
horizontal shift left
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transformation form
f(x)=(x-h)+k
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sequence
an ordered list of numbers that forms a pattern
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arethmatic sequence
has a common difference between each term in sequence
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recursive formula
a1=___; an = an-1 + d
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explicit formula
 an = a + (n - 1)d
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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.
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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.
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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.
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line of best fit
trend line that matches the data/points the greatest
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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.
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bivariate data set
data set with 2 variables
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residual
difference between the y-value and the corresponding y-value
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interpolation
using a model to estimate a value within the range of known values
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extrapolation
using a model to make a prediction about a vaule outside of known values
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causation
describes a cause and effect relationship
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product of powers
knowt flashcard image
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quotient of powers
knowt flashcard image
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power of product
knowt flashcard image
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negative exponents
knowt flashcard image
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0 exponent
equal to 1
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rational exponents
knowt flashcard image
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graphing exponential functions
f(x)=ab^x
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exponential growth
f(x)= a(1+r)^x
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compound interest
a=p(1+r/n)^nt
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exponential decay
f(x)=a(1-r)^x
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geometric recursive formula
an=(an-1)(r)
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geometric explicit formula
an=(a1)(r^n-1)
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transformin exponential functions
f(x)=a^(x-h)+k
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polynomial
a monomial or the sum or difference of two or more monomials called terms
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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.
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finding vertex
(-b/2a,f(-b/2a))
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standard form
f(x)=ax^2+bx+c
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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.
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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.
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completing a square
(b/2)^2
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quadratic formula
x = (-b ± √(b² - 4ac)) / 2a
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vertex form
f(x) = a(x-h)^2 + k
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finding x intercepts
make Y 0

EXP: 0=2x^2+6x+5
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finding y intercept
evauate x for 0

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

f(0)=5