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Algebra Cheat Sheet
Basic Properties & Facts  
Arithmetic Operations Exponent Properties Properties of Radicals

Properties of Inequalities Properties of Absolute Value Triangle Inequality Distance Formula

Logarithms and Log Properties  
Definition is equivalent to Example because Special Logarithms natural log common log where e = 2.718281828K 
Logarithm Properties
The domain of 
Factoring and Solving  
Factoring Formulas
If n is odd then

Quadratic Formula Solve ax ^{2} + bx + c = 0, a ≠ 0 If b^{2}  4ac > 0  Two real unequal
solns. 
Completing the Square  
Solve 2x^{2}  6x 10 = 0 (1) Divide by the coefficient of the x^{2 } x^{2}  3x  5 = 0 (2) Move the constant to the other side. x^{2}  3x = 5 (3) Take half the coefficient of x, square it and add it to both sides

(4) Factor the left side (5) Use Square Root Property (6) Solve for x 
Functions and Graphs  
Constant Function Slope – intercept form 
Parabola/Quadratic Function x = ay^{2} + by + c g ( y) = ay^{2} + by + c The graph is a parabola that opens right if a > 0 or left if a < 0 and has a vertex at .
Circle Graph is a hyperbola that opens left and Graph is a hyperbola that opens up and 
Common Algebraic Errors
Error  Reason/Correct/Justification/Example 
and  Division by zero is undefined ! 
Watch parenthesis !  
A more complex version of the
previous error 

Beware of incorrect canceling! 

Make sure you distribute the ““! 

See previous error .  
and  More general versions of previous
three errors. 
Square first then distribute! 

See the previous example. You can not factor out a constant if there is a power on the parethesis ! 

Now see the previous error. 

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