Formula Sheet for Blitzer's College Algebra

This formula sheet is intended as a resource for common algebra notation and symbols .
This formula sheet is not intended as a comprehensive review of all theorems and
procedures covered in the textbook.

Chapter 2: Functions & Their Graphs

Note: increasing, decreasing, and constant intervals are always defined as open sets, that
is, these intervals use parentheses, not brackets.

Difference Quotient :
Composition of Functions:
Inverse Functions:

Chapter 3: Polynomial Functions

You are expected to know by memory the quadratic formula (p.137)

Vertex Formula:
Standard Form of a Quadratic Function:	y = a(x − h)2 + k
Turning Points (Hills & Valleys):	n – 1
Horizontal Asymptotes:

Chapter 4: Exp onential & Linear Functions

You are expected to know by memory the properties of exponents (p.23)

Definition of Logarithms:	If then
Addition Property of Logarithms:
Subtraction Property of Logarithms:
Power Property of Logarithms:
Compound Interest Formula:
Exponential Growth /Decay:

Chapter 8: Sequences and Series

Sum of the first n terms of sequence an:
Arithmetic Sequences & Series:
Geometric Sequences & Series:
Infinite Geometric Series:

Other Useful and Interesting Formulas in Word Problems

Distance d traveled at speed r and time t:	d = rt
Speed V (mph) of car based on skid length L (feet):
Distance d (miles) to the horizon at a given height h (feet):
Distance d (miles) to lightening in t (seconds) from thunder clap:
Child dosage C based on child’s age A and adult dosage D:
Body surface area based on h (inches) and w (pounds):
Ideal male body weight w (kg) in terms of height h (inches):	w = 51.85 +1.85(h − 60)
Ideal female body weight w (kg) in terms of height h (inches):	w = 48.67 +1.65(h − 60)
Simple Interest Formula:	A = P(1+ rt )
Rule of 70 for doubling time t at a given APR (%):
Rule of 3 for Decibel scale:	3+ dB→2× volume
Age in space S at velocity v (mph) vs. age on earth E:
Height h (feet) of a ball, body, etc. after falling t seconds:
Average of two speeds and (harmonic mean):
Average of two interest rates and (geometric mean):
Area of an ellipse :	A =π ab
Area under a parabola b units across and h units high:
Max area of a 3-sided or 4-sided rectangular pen with perimeter P: