Algebra Cheat Sheet

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

 

The domain of

If n is odd then

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

(4) Factor the left side

(5) Use Square Root Property

(6) Solve for x

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 .