# Algebra Cheat Sheet

 Basic Properties & Facts Arithmetic Operations Exponent Properties Properties of Radicals ,if n is odd ,if n is even Properties of Inequalities If then and If and then and If and then and Properties of Absolute Value Triangle Inequality Distance Formula If and are two points the distance between them is Complex Numbers Complex Modulus Complex Conjugate 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 b2 - 4ac > 0 - Two real unequal solns. If b2 - 4ac = 0 - Repeated real solution. If b2 - 4ac < 0 - Two complex solutions. Square Root Property If x2 = p then Absolute Value Equations/Inequalities If b is a positive number Completing the Square Solve 2x2 - 6x -10 = 0 (1) Divide by the coefficient of the x2 x2 - 3x - 5 = 0 (2) Move the constant to the other side. x2 - 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 y = a or f ( x) = a Graph is a horizontal line passing through the point (0, a) . Line/ Linear Function y = mx + b or f ( x) = mx + b Graph is a line with point (0,b) and slope m. Slope Slope of the line containing the two points and is Slope – intercept form The equation of the line with slope m and y-intercept (0,b) is y = mx + b Point – Slope form The equation of the line with slope m and passing through the point is Parabola/Quadratic Function The graph is a parabola that opens up if a > 0 or down if a < 0 and has a vertex at (h, k ) . Parabola/Quadratic Function y = ax2 + bx + c f (x ) = ax2 + bx + c The graph is a parabola that opens up if a > 0 or down if a < 0 and has a vertex at Parabola/Quadratic Function x = ay2 + by + c g ( y) = ay2 + by + c The graph is a parabola that opens right if a > 0 or left if a < 0 and has a vertex at .   Circle ( x - h)2 + ( y - k )2 = r2 Graph is a circle with radius r and center (h, k ) . Ellipse Graph is an ellipse with center (h, k ) with vertices a units right/left from the center and vertices b units up/down from the center. Hyperbola Graph is a hyperbola that opens left and right, has a center at (h, k ) , vertices a units left/right of center and asymptotes that pass through center with slope . Hyperbola Graph is a hyperbola that opens up and down, has a center at (h, k ) , vertices b units up/down from the center and asymptotes that pass through center with slope .

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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