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  • 8/10/2019 Math Resources Algebra Formulas

    1/4

    Algebraic Formula Sheet

    Arithmetic Operations

    ac+bc= c(a+b)

    ab

    c =

    a

    bc

    a

    b+

    c

    d=

    ad+bc

    bd

    a bc d =

    b ad c

    ab+ac

    a =b+c, a = 0

    a

    b

    c

    =

    ab

    c

    ab

    c

    =

    ac

    b

    a

    c c

    d=

    ad bcbd

    a+b

    c =

    a

    c+

    b

    c

    ab

    c

    d

    = adbc

    Properties of Exponents

    xnxm =xn+m

    (xn)m = xnm

    (xy)n =xnyn

    xn

    m =

    x 1

    m

    n=

    xn 1

    m

    x

    y

    n

    =

    y

    x

    n=

    yn

    xn

    x0 = 1, x = 0

    xy

    n

    =

    xn

    yn

    1

    xn =xn

    xn

    xm =xnm

    xn = 1

    xn

    Properties of Radicals

    n

    x= x1

    n

    n

    xy= n

    x n

    y

    mn

    x= mn

    x

    n

    x

    y =

    n

    x

    n

    y

    n

    xn =x, ifn is odd

    n

    xn =

    |x

    |, ifnis even

    Properties of Inequalities

    Ifa < b then a+c < b+c and a c < b c

    Ifa < b and c >0 then ac < bc and a

    c

    b

    c

    Properties of Absolute Value

    |x| =

    x ifx 0x ifx

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    Logarithms and Log Properties

    Definition

    y = logbx is equivalent to x= by

    Example

    log216 = 4 because 24 = 16

    Special Logarithms

    ln x= logex natural logwhere e=2.718281828...

    log x= log10x common log

    Logarithm Properties

    logbb= 1

    logbbx

    =x

    ln ex = x

    logb1 = 0

    blog

    bx

    =x

    elnx =x

    logb(xk) = klogbx

    logb(xy) = logbx+ logby

    logbxy = logbx logby

    Factoring

    xa+xb= x(a+b)

    x2 y2 = (x+y)(x y)

    x2 + 2xy+ y2 = (x+y)2

    x

    2

    2xy+y2

    = (x y)2

    x3 + 3x2y+ 3xy2 +y3 = (x+y)3

    x3 3x2y+ 3xy2 y3 = (x y)3

    x3 +y3 = (x+y)

    x2 xy+ y2x3 y3 = (x y) x2 +xy+y2x2n y2n = (xn yn) (xn +yn)

    Ifn is odd then,

    xn yn = (x y) xn1 +xn2y+...+yn1xn +yn = (x+y)

    xn1 xn2y+ xn3y2... yn1

    Linear Functions and Formulas

    Examples of Linear Functions

    x

    y

    y= x

    linear function

    x

    y

    y= 1

    constant function

    2

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    Constant Function

    This graph is a horizontal line passingthrough the points (x, c) with slope m= 0 :

    y = c or f (x) =c

    Slope (a.k.a Rate of Change)

    The slope mof the line passing throughthe points (x1, y1) and (x2, y2) is :

    m=y

    x=

    y2 y1x2 x1 =

    rise

    run

    Linear Function/Slope-intercept form

    This graph is a line with slope mand y intercept(0, b) :

    y = mx+b or f (x) =mx+b

    Point-Slope form

    The equation of the line passing throughthe point (x1, y1) with slope mis :

    y = m(x x1) +y1

    Quadratic Functions and FormulasExamples of Quadratic Functions

    x

    y

    y= x2

    parabola opening up

    x

    y

    y= x2

    parabola opening down

    Forms of Quadratic Functions

    Standard Form

    y= ax2 +bx+cor

    f(x) =ax2 +bx+c

    This graph is a parabola thatopens up ifa >0 or down if

    a 0 or down if

    a

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    Quadratics and Solving for x

    Quadratic FormulaTo solve ax2 +bx+c= 0, a = 0,use :

    x=b b2 4ac

    2a .

    The DiscriminantThe discriminant is the part of the quadraticequation under the radical, b2 4ac. We usethe discriminant to determine the number ofreal solutions ofax2 +bx+c= 0 as such :

    1. Ifb2 4ac >0, there are two real solutions.2. Ifb2 4ac= 0, there is one real solution.3. Ifb2 4ac