math resources algebra formulas
TRANSCRIPT
-
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
-
8/10/2019 Math Resources Algebra Formulas
2/4
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
-
8/10/2019 Math Resources Algebra Formulas
3/4
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
-
8/10/2019 Math Resources Algebra Formulas
4/4
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