Algebra Review

Linear Equations
Standard Form of an Equation -- Ax + By = C
Slope-Intercept Form of an Equation -- y = mx + b
Calculating Slope -- m = y - y1 / x2 - x1
Point Slope Formula -- y - y1 = m (x -x1)
Distance Formula -- D = ¯(x2 - x1)2 + (y2 - y1)2
Midpoint Formula -- ( x1 + x2 /2, y1 + y2 /2 )
Factoring
Difference of Two Squares
a2 - b2 = (a + b)( a - b)
Perfect- Square Trinomials
a2 + 2ab + b2 = (a + b)2
a2 - 2ab + b2 = (a - b)2
Sum of Two Cubes
a3 + b3 = (a + b)(a2 - ab + b2)
Difference of Two Cubes
a3 - b3 = (a - b)(a2 + ab + b2)
Powers
Multiplication
---(xa)(xb) = xa+b
Division
---xa ÷ xb = xa-b
Zero and Negative
---x0 = 1
---x-a = 1/ xa
Others
---(xa)b = xab
---(xy)a = xa ya
---(x/y)a = xa / ya
Fractions
---x1/a = a¯ x
Conic Sections
Circles
---Standard Form (x - h)2 + (y - k)2 = r2 (h,k) is the center
---General Form x2 + y2 + Dx + Ey + F = 0
D = -2h E = -2k F = h2 + k2 - r2
Parabolas
Standard Form x2 = 4py
focus (0, p) and directrix y = -p
or
y2 = 4px
focus (p,0) and directrix x = -p
Ellipses
Standard Form x2 / a2 + y2 / b2 = 1
foci (-c,0) and (c,0) with a2 = b2 + c2
Hyperbola
Standard Form x2 / a2 - y2 / b2 = 1
foci (-c,0) and (c,0) with c2 = a2 + b2

Logarithms
Common logarithm (log) base is 10
Natural logarithm (ln) base is
e Logx a = b so that xb = a

Quadratic Formula
x = -b ± ¯b2 - 4ac 2a