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College Algebra and Trig
Chapter 2
14
Mathematics
Undergraduate 1
09/21/2010
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Term
Quadratic Function
 Definition
f(x)=ax2+bx+c
Term
Standard Form of f(x)
 Definition

f(x)=a(x-h)2+k

h=(-b)/(2a)

k=(4ac-b2)/(4a)

Vertex: (h,k)
Term
The parabola opens upward if...
 Definition
a>0
Term
The parabola opens downward if...
 Definition
a<0
Term
Axis of Symmetry
 Definition
x=h
Term
when n is an odd number and a>0
 Definition

x -> -∞, anxn -> -∞ (falls to the left)


x -> +∞, anxn -> +∞ (rises to the right)
Term
n is odd and an<0
 Definition

 

x -> -∞, anxn -> +∞ (rises to the left)


x -> +∞, anxn -> -∞ (falls to the right)

 
Term
n is even and an>0
 Definition

 

x -> -∞, anxn -> +∞ (rises to the left)


x -> +∞, anxn -> +∞ (rises to the right)

 
Term
n is even and an<0
 Definition

x -> -∞, anxn -> -∞ (falls to the left)


x -> +∞, anxn -> -∞ (falls to the right)
Term
i=(-1)1/2
 Definition

a is called the real part

b is called the imaginary part

 

if b=0, a+bi = a is a real number

if b≠0, a+bi = is imaginary number
Term
(a+bi) + (c+di)
 Definition
=(a+c) + (b+d)i
Term
(a+bi) - (c+di)
 Definition
=(a-c) + (b-d)i
Term
(a+bi)(c+di)
 Definition
=ac+adi+bci+bdi3
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