Algebra 2 basics

circle equation

(x-h)^2 + (y-k)^2 = r^2

How to solve an arithmetic sequence when given 2 points

-change of y2-y1 - x2-x1 (to find slope) - work backwards to find term 0

What methods do you use when solving an equation?

-equal values -substitution -elimination

How to simplify rational expressions:

-factor -cross out like values

How to solve an equation with x^2 in it

-square root -factor -quadratic formula

Compound equation

A=p(1+r) ^n*t n

What to do with exponents to simplify when given expressions like: (6x^4 y^12)(2x^2 y^5)

Add exponents

What to do with exponents to simplify when given expressions like: (-5xy^2)^3

Multiply exponents

factored form

Y=(x+___)(x+__)

Exponential function equation

Y=a(b)^x

Graphing form

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

Cube root equation

Y=a(x-h)^3+k

Absolute value equation

Y=a|x-h|+k

standard form

y=ax^2+bx+c

How to complete an exponential table when given two points

1: count # of gaps between your 2 x values and that is the exponent with b Ex: 2 points: (1,10) (4,1250) 4-1=3 B^3 2: put 1st y-value before b and = it to 2nd y-value Ex: 10b^3=1250 3: solve normally to find b (b=5) 4: plug b (5) into y=a(b)^x equation and replace the y with a y-value on the table Ex: 10=a(5)^x 5: solve normally to find a 6: use equation to find other missing table values

How to simplify a radical

1: find 2 #'s that * to the number under the square root, one of them has to be able to be square rooted Ex: (sr)40 can be broken down to (sr)4 and (sr)10 2: square root the # that is able to be square rooted whole Ex: 2, then (sr)10 3: include the whole square rooted # outside of the square root sign, with the non-whole # under the square root Ex: 2(sr)10 4: simply other exponents as well Ex: x^2 y^4 =xy^2

What to do when a system of equations CANNOT be solved by substitution or equal values

1: multiply one of the equations do that 1 variable cancels out in both equations Ex: 2(2x-y=5). 4x-2y=10 5x+2y=8 + 5x+2y=8 2: solve for the remaining variable 3: plug in variable value to original equation and solve for remaining variable

How to graph and solve an inequality

1: treat the > and < signs as if they're = signs and solve for x and y values like you normally would 2: graph intercepts: > = open dot 3: plug in a point to the equation ( like 0,0 ) and if it works you INCLUDE that point in the shading!

How to SOLVE radical expressions

1: variable goes under square root (or the base) 2: top # of fraction pairs w/variable inside square root 3: bottom # of fraction goes outside sr Ex: g ^3/2 2(sr)g^3