ALGEBRA 2 SOL REFERENCE SHEET
This you need to memorize for the SOL test.

GOLDEN RULE:
If it is in a parenthesis—DO THE OPPOSITE!!!
Properties
Commutative Property 3+5=5+3 3*5=5*3 (change order)
Associative property (3+4) +5 = 3+ (4+5) same for multiplication (grouping)
Identity Property a*1= a
a+0=a (What you start with is what you end with)
Distributive Property 3(a+8) = 3a+24
Multiplicative Property of Zero x*0=0
Reflexive property IF ab=4 THEN ab=4 (the same on both sides)
Symmetry property IF xy=6 THEN 6=xy (flipped ---Has to have the if then)
Transitive If x+2=y and y=6 then x+2=6 (three items)

𝑦>0
Function Families:
Linear (/ ),Quadratic (U), Absolute value (V), Rational (2 curves) , exponential
Polynomial
Odd degree
Even degree
Square root
, Logarithmic
𝑦≥0
 Interval of Increasing or decreasing
 Use only the X values and look at the graph to decide where it is increasing or decreasing

End behavior= What direction the graph going at the ends.
f(x)

___ as x
The turning
point is where
the graph
turns-I use
that for
increasing or
decreasing
_____ Use +∞ or -∞ for the blanks
or numbers for Roots, Logs, Expos
Parent Functionso Horizontal shift if the number is changing the x “Golden Rule”
o Vertical shift is the number that is not with the x

Absolute value equations- 2bars 2 equations! Look out for bars equaling a negative number
That’s a {no solution}
 Variations
Direct Variation-Where the line goes through the origin. Also uses y=kx, where k is the constant (slope)
Indirect/Inverse Variation- y 
k
(division)
x
Did I
remember to
divide at the
end?
Joint Variation- y=kxz (Needs two or more items)
Don’t forget the EARMUFF method for
 Polynomials Standard form ax2+bx+c=0 highest degree 1st
trinomials with a leading coefficient.
Degree of polynomial is the largest exponent.
 FACTOR—Check for GCF first (could be # or variable or both)
Sign rules for factoring ___ + ___ + ____
DOPS
This sign is the result when you
add the two factors together
If you see (+) Add or (-) subtract the
factors to make the middle number
Difference of Perfect Squares x2-4 (prefect square) - (perfect square)
Perfect trinomials ( + )2 signs are the same, either + or –
Difference of cubes x3  8 = ( x  2)( x 2  4 x  4) “alternate signs”

Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key
Maximum Opens Down a<0
Minimum Opens up a>0
If a=0 then it’s a linear equation not a parabola (u shaped)
Vertex ( , ) where the min and max is located. Go to y= then graph, 2nd trace choose max or min then
hit enter, enter, enter.
Axis of symmetry always is x=(the first coordinate of the vertex)
The following all mean the same thing—
Crosses the x axis----Table (look for zeros or sign changes in the y column)
Zero of the function
Factors
Real solutions
x-intercepts
Roots

Zero of function---what would x equal to make the function equal zero
Where does the graph cross the x-axis?
−𝑏±√𝑏2 −4𝑎𝑐
Quadratic Formula---- 𝑥 =
2𝑎
FACTORING DOESN”T WORK
CAN BE USE TO SOLVE FOR X WHEN
DIGGIN’ Up Holes
 Vertical Asymptotes-where the graph cannot have a zero is the denominator
1
, VA x= 2
 x  2
“Golden Rule”
 Point discontinuity (hole)-When a binomial gets cancelled out. “Golden Rule”
 Horizontal asymptotes-3 conditions
1.
If the degree is the same then the number in front remains y= the coefficients
2.
Higher degree on top then the asymptote is a flop y=none
3.
Higher degree is below then y=0
 Scatter plots or best fit of line
1. For Linear Functions-go to STAT EDIT CAL 4 ENTER
2. For Exponential –go to STAT EDIT CAL 0 ENTER

Rational Functions-Must have like denominators to add the numerators. Sometimes you have to
factor to see the new denominator.
Remember: What you see is what you need for the LCD!!
(Do not do this for multiplying and dividing)
 Sequences and Series
Arithmetic sequence an  a1  (n  1)d
a1 means the first term
d means the difference between terms
For DIVIDING
geometric sequence an  a1  r n 1
n means the number of terms
r means the multiplying ratio between terms
end
Find it
under
Math
PROB
button
in cal.
Series (summation)-
 formula
start
Probability and Stats
Permutation- nPr Used when a few out many are selected for specific Positions
Combinations – nCr used when only a few out a group are needed, no specific order.
Standard Deviation- the gap between intervals from the MEAN of the data
Factorial –n! used when all the items are used in the arrangement
BFF
Better
Factor
Firstt