Alegbra 2

In systems of equations, how many solutions do parallel lines have?

0 solutions

Inconsistent

0 solutions

row 0 of pascals triangle

1

row 1 of Pascal's triangle

1 1

row 2 of Pascal's triangle

1 2 1

(7 + x ) + y = 7 + ( x + y )

Associative

Arithmetic Mean

Average of 2 numbers the difference between n-1 and n+1 divided by 2 and added to n-1

Standard form

Ax + By = C

Classify a polynomial w degree of X^0

Constant

6 + ( -6 ) = 0

Inverse property of addition

Classify a polynomial w degree of X^1

Linear

Slope formula

M = (y2 - y1) / (x2 - x1)

Absolute Value Graph what's your transformation for the 2nd "2" in 2|x+3|+2

Shift up vertically by 2

formula to find sum of geometric series

Sn = (a(1) (1-r^n) ) / (1-r) n = terms (a(n))

Which formula do you need to know for word problems

Sn = (a(1) (1-r^n) / (1-r)

Arithmetic Series Formula

Sn = (n/2) (a1 + an)

How do you solve an absolute value equation

Split into 2 inequalities Solve each equation Check each solution in the original equation

what is the sigma symbol used to indicate

Summation Notation indicates adding

If 5 = 4 + 1, then 4 + 1 = 5

Transitive property

Explicit Formula for Arithmetic Sequence

an = a1 + (n-1)(d)

Recursive Formula for Arithmetic Sequence

an = an-1 + d a1 =

How does a polynomial react w/ x-axis when there is a multiplicity of 2

bounce off

Consistent

dependent and independent

If the discriminant is positive,

it has two solutions

X ^m / n - power

m

next steps to solve 3^3x-4 = 7

multiply by log log 3^3x-4 = log 7 3x-4 log 3 = log 7 divide the logs solve for x

How do you find the number on top of sigma?

use the formula to side of sigma... if (x(n) - y)....add y to last term if (x(n) + y)....subtract y from last term then divide that by x

equation if y varies directly as x and inversely as z

y = kx / z

vertex

( h , k )

X ^ m / n in radical form

( n √x ) ^m

(√7x) ^3 in x ^m / n

((7x) ^1 / 2) ^3

domain for rational expressions

(- infinity , vertical asymptote) U ( vertical asymptote , vertical asymptote) U ( vertical asymptote , infinity )

y intercept is (x , 0) or (0 , x)

(0 , x)

√(7x)^3 in x ^m / n form

(7x) ^3 / 2

steps to put vertex to standard

1. 4 (x - 1)^2 + 5 2. 4 { (x-1)(x-1) } + 5 3. 4 (x^2 - 2x + 1) + 5 4. 4x^2 - 8x + 4 + 5 5. 4x^2 - 8x + 9

steps to put standard to vertex

1. identify a b & c 2. find x-coordinate of vertex (h=-b/2a) 3. plug value in where x is 4. y = k 5. plug in h value and k value into vertex form

Dependent

2 - infinite solutions

after X method.. to simplify

3x^2 + 4x - 6x - 8 | 3x^2 + 4x | | - 6x - 8 | GCF x ( 3x + 4 ) - 2 ( 3x + 4 ) ( x - 2 ) ( 3x + 4 )

index of ⁵√x

5

√5 • ⁵√5

5 ^1 / 2 • 5 ^1 / 5 5 ^5 / 10 • 5 ^2 / 10 5 ^7 / 10 10√5 ^7

√7x^3 in x ^m / n form

7 ^1 / 2 X ^3 / 2

sum of perfect cubes a ^3 + b ^3

(a + b)(a ^2 - ab + b^2)

difference of perfect squares a ^2 - b ^2

(a - b)(a + b)

difference of perfect cubes a ^3 - b ^3

(a - b)(a ^2 + ab + b ^2)

Exponential Formula for Geometric Sequences

(a)n = (a)1 • r^n-1

Recursive Formula for Geometric Sequences

(a)n = (a)n-1 • r

x intercept is (x , 0) or (0 , x)

(x , 0)

If systems of equations is linear, how many solutions?

1 solution

Independent

1 solution

if the graph is shaded below the line, what is the inequality symbol?

< , less than

if the graph is shaded above the line, what is the inequality symbol?

> , greater than

when you see "continuously" in a word problem, you should use what equation?

A =Pe^rt

Fundamental Theorem of Algebra

A polynomial will have as many roots as its degree

what is this fifth step of solving an absolute value equation, after you have made your t-table

Choose x-values, 2 above and 2 below the middle x - value

Classify a polynomial w degree of X^3

Cubic

( 15 x + 5 ) = 5 ( 3x + 1 )

Distributive

Relation

Domain number appears twice

How to do rational root theorem

First set up p / q chart Calc: put equation in regular screen use numbers in p / q 1 , STO> , X , if = 0 , a root use number that equaled zero and divide synthetic division use polynomial you found and plug into quadratic formula get solutions

What is the first step in solving an absolute value equation

Get the equation into the form of y =

(a + b)( 1 ) = (a + b)

Identity property of multiplication

what is the fourth step of solving an absolute value equation, after you have found the vertex

Make a t-table. Put the vertex in the middle

Absolute Value Graph what's your transformation for |x+3| in 2|x+3|+2

Move to the left 3 points

what is the first step in solving for b when A = 1/2h (a + b)

Multiply by 2 2A = h (a + b)

How do you find the next term in a Geometric Sequence?

Multiply the previous term by the common ratio (r)

Function

Only one number of each domain

what is the third step of solving an absolute value equation, after you have solved for x. what have you just found?

Plug the Middle x-value into the original equation to find y. The point (x,y) that you have just found is the vertex

Classify a polynomial w degree of X^2

Quadratic

Classify a polynomial w degree of X^4

Quartic

Classify a polynomial w degree of X^5

Quintic

( 3 + 4 ) + 7 = ( 3 + 4 ) + 7

Reflexive

Formula for infinite geometric and arithmetic series

S (infinity) = (a(1)) / (1-r)

what is the difference between a series and a sequence

Sequence - an ordered list, commas Series - sum of a list, plus signs

what is the second step of solving an absolute value equation, after you have got the equation into y =

Set what's inside the absolute value sign equal to zero. Solve for x.

when is the no horizontal asymptote?

X^3 +5 / x^2 - 1

can you multiply and divide radical expressions if the index is the same?

Yes

Simplify b = (2A - ha) / h

b = (2A/h) - a

Discriminate

b^2 - 4ac

logb a = x can also be written as

b^x = a

What are you finding in a Arithmetic Sequence?

d= common difference

how to write equation from graph

degree is one more number than how many turning points find roots factors from roots multiply factors together

what is the next step in solving for b when 2A = h (a + b)

distribute h 2A = ha + hb

what is the next step in solving for b when 2A - ha = hb

divide by h b = (2A - ha) / h

how to find horizontal asymptote

divide the highest degree number

quadratic parent function

f (x) = x^2

write polynomial with roots x = 3, multiplicity 3

f(x) = (x - 3)^3

vertex form

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

standard form for quadratics

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

how to find the vertical asymptote

factor the denominator and set equal to zero

How do you find the arithmetic mean

find the average... subtract right number from left divide the difference by 2 add difference to left number

what is the sixth step of solving an absolute value equation, after you have chosen x-values

find the y values to complete the table

to find min or max

find the y-value of ( x , y ) (but put in x= )

steps to solve e^x/5 +4 = 7

get e^x/5 alone e^x/5 = 3 get rid of e ( • ln) (ln) (e^x/5) = (ln)3 x/5 = ln3 solve for x

steps to solve ln(x-1 / 3) = 4

get rid of ln by multiplying by e (e) ln(x-1 / 3) = 4 (e) 4 (e) becomes e^4 (x-1 / 3) = e^4 solve for x

to find zeros..

graph in calculator or.. set (x-5) = 0 solve for x

to find h for translating standard to vertex

h = -b / 2(a)

Rule of Signs

how ever many times the signs change, is how many possible solutions

what does the number on top of sigma mean?

how many terms are in the list... a(n)

How do you know if a series converges or diverges?

if r<1 converges if r>1 diverges if r=1 then neither

direct variation

if y varies directly as x y = kx

inverse variation

if y varies inversely as x k = xy

If the discriminant is 0,

it only has one solution.

steps to solve log 3 + log x = 4

log 3x = 4 can also be written as 3x = 10^4 solve for x

log3x = 4 can also be written as

log10 (3x) =4 (3x) = 10^4

X ^ m / n - root / index

n

do you need to solve | x - 3 | > -4 ?

no, all real numbers

do you need to solve | x - 3 | < -4 ?

no, it's no solution

Rational Root Theorem

p / q p = factors of constant q = factors of leading coefficient

What are you finding in a Geometric Sequence?

r= common ratio

Solve by completing the square 3x^2 - 12x + 6

rewrite in x^2 + bx = c divide so a = 1 Add ( b / 2 )^2 to both sides Factor ( ( b / 2 ) ) Square root Plus or Minus!!! Split into two and solve

when you're given a number, and you're finding what nth it is.. how do you find the nth

set the number that you're given equal to your explicit formula and solve for n

Rational Root Theorem w no calc

set up p / q chart rule of signs to possibly eliminate use synthetic division and go through (p / q) list is remainder is zero, you have a factor set polynomial you found = 0 or quadratic formula solutions

to find y intercept

set x equal to 0 (x=0)

to find x intercept

set y equal to 0 (y=0)

Geometric Mean

square root of n-1 and n+1

How does a polynomial react w/ x-axis when there is a multiplicity of 1

straight through

what is the next step in solving for b when 2A = ha + hb

subtract ha 2A - ha = hb

How does a polynomial react w/ x-axis when there is a multiplicity of 3

swerve

If the discriminant is negative,

the answer is no solution.

Arithmetic indicates what

the difference is the same between every number

Absolute Value Graph what's you're transformation for the first 2 in 2|x+3|+2

the the slope, slope of 2

After you have set what is in the | absolute value | sign to 0 and have solved, what is the number that you have come up with?

this is known as the middle x-value

When do you need the recursive formula

to find a term in the past

When do you need the exponential formula

to find the nth term in the future (....)

how do you find the formula to the side of sigma for arithmetic?

use explicit formula and simplify to (x(n) + y)

Remainder Theorem

when f(x) is divided by (x-a) the remainder is f(a) when you divide a polynomial by (x-3) then the number you get after you plug 3 into the polynomial is your remainder

radicand of ⁵√x

x

How do you find the Geometric mean

x , ________ , y \|(x)(y) Multiply left term and right term and and square it

Domain

x - value side to side

Quadratic Formula

x = [ -b ± √(b² - 4ac) ] /2a

axis of symmetry

x = h

End behavior of negative coefficient, even degree

x → ∞ y → -∞ x → -∞ y → -∞

End behavior of negative coefficient, odd degree

x → ∞ y → -∞ x → -∞ y → ∞

End behavior of positive coefficient, odd degree

x → ∞ y → ∞ x → -∞ y → -∞

End behavior of positive coefficient, even degree

x → ∞ y → ∞ x → -∞ y → ∞

is vertical asymptote x= or y=

x=

simplify x⁵ y^2 z^-6 / x^-3 y^5 z^2

x^8 / y^3 z^8

in a word problem for direct/inverse variation what variable is dependent and what variable is independent

y - dependent x - independent

Range

y - values up to down

Slope intercept form

y = mx + b

joint variation

y varies jointly with x and z y = kxz

Point slope form

y-y1=m(x-x1)

is horizontal asymptote x= or y=

y=