Phi 208 week 3 discussion 2

GEOMETRIC FORMULAS

Formulas for area A, perimeter P, circumference C, volume V :

Rectangle Box

A � l„ V � l„ h

P � 2l � 2„

Triangle Pyramid

A � �1 2

� bh V � �1 3

�ha2

Circle Sphere

A � �r 2 V � �4 3

��r 3

C � 2�r A � 4�r 2

Cylinder Cone

V � �r 2h V � �1 3

��r 2h

HERON’S FORMULA

Area � �s 1�s��� a�2 1�s��� b�2 1�s��� c�2� where s � �

a � 2 b � c �

hh

r

r

r r

h

b a a

h

„

l

h

l „

EXPONENTS AND RADICALS

xmxn � xm�n � x x

m

n� � x m�n

1xm2n � xm n x�n � � x 1

n�

1xy2n � xnyn a�xy�b n

� � x y

n

n�

x1�n � �n x� xm�n � �n xm�� � Q�n x�Rm

�n xy� � �n x� �n y� �n xy��� � �

n x�

�n y� ��

�m �n��x� ��n �m��x� � �mnx�

SPECIAL PRODUCTS

1x � y22 � x 2 � 2xy � y 2 1x � y22 � x 2 � 2xy � y 2 1x � y23 � x 3 � 3x 2y � 3xy 2 � y 3 1x � y23 � x 3 � 3x 2y � 3xy 2 � y 3

FACTORING FORMULAS

x 2 � y 2 � 1x � y2 1x � y2 x 2 � 2xy � y 2 � 1x � y22 x 2 � 2xy � y 2 � 1x � y22 x 3 � y 3 � 1x � y2 1x 2 � xy � y 22 x 3 � y 3 � 1x � y2 1x 2 � xy � y 22

QUADRATIC FORMULA

If ax 2 � bx � c � 0, then

x �

INEQUALITIES AND ABSOLUTE VALUE

If a � b and b � c, then a � c.

If a � b, then a � c � b � c.

If a � b and c � 0, then ca � cb.

If a � b and c � 0, then ca � cb.

If a � 0, then

⏐x⏐ � a means x � a or x � �a.

⏐x⏐ � a means �a � x � a.

⏐x⏐ � a means x � a or x � �a.

�b �b�2��� 4�a�c� ��

2a

b

B

CA

ac

DISTANCE AND MIDPOINT FORMULAS

Distance between P11x1, y12 and P21x2, y2 2 : d � � 1x�2��� x�12�2��� 1�y2� �� y�12�2�

Midpoint of P1P2: a�x1 � 2

x2. �, �

y1 �

2

y2. �b

LINES

Slope of line through P11x1, y12 and P21x2, y2 2 Point-slope equation of line y � y1 � m 1x � x12 through P11x1, y12 with slope m Slope-intercept equation of y � mx � b line with slope m and y-intercept b

Two-intercept equation of line with x-intercept a and y-intercept b

LOGARITHMS

y � loga x means a y � x

loga a x � x a loga x � x

loga 1 � 0 loga a � 1

log x � log10 x ln x � loge x

loga xy � loga x � loga y loga a�xy�b � loga x � loga y loga x

b � b loga x logb x �

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

0

1

y=a˛ 0

0

1

y=a˛ a>1

1

y=loga x a>1

0

y=loga x 0

10

y

x

y

x

y

x

y

x

loga x

log a b

� a x

� � � b y

� � 1

m � � x

y2

2

�

�

y

x 1

1 �

GRAPHS OF FUNCTIONS

Linear functions: f 1x2 � mx � b

Power functions: f 1x2 � xn

Root functions: f 1x2 � �n x�

Reciprocal functions: f 1x2 � 1/xn

Absolute value function Greatest integer function

Ï=“x ‘

1

1

x

y

Ï=|x |

x