Chapter 3 Flashcards
quadratic form
f(x)=ax^2+bx+c
standard form
f(x)=a(x-h)^2+k
intercept form
f(x)=a(x-p)(x-q)
quadratic form a.o.s.
-b/2a
quadratic form vertex
(-b/2a, f(-b/2a))
standard form a.o.s.
h
standard form vertex
(h, k)
intercept form a.o.s.
(p+q)/2
intercept form vertex
((p+q)/2, f((p+q)/2))
End Behavior:
Positive Even
Field Goal
End Behavior:
Negative Even
Rainbow
End Behavior:
Positive Odd
Up towards the right
Down towards the left
End Behavior:
Negative Odd
Down towards the right
Up towards the left
number of positive real zeros
(Descarte’s Rule of Signs)
Number of variations in signs of P(x) or less by an even whole number
number of negative real zeros
(Descarte’s Rule of Signs)
Number of variations in signs of P(-x) or less by an even whole number
Upper bound
Divide P(x) by x-b (b>0) using synthetic division and if the row has no negatives, b is an upper bound
Lower Bound
Divide P(x) by x-b (b<0) using synthetic division and if the row have alternately positive and negatives, b is a lower bound
Fundamental Theorem of Algebra
Every polynomial with complex coefficients has at least one complex zero
Multiplicity
If the factor x-c appears k times, we say c is a zero of multiplicity k
Zeros Theorem
Every polynomial of degree n>1 has exactly n zeros
Complex Zeros Theorem
If the polynomial P has real coefficients, and if the complex number z is a zero of P, then its complex conjugate is also a zero of P
Linear and Quadratic Factors Theorem
Any polynomial with real coefficients can be factored into a product of linear and quadratic factors with real coefficients
