Chapter 2 – Polynomial and Rational Functions
The axis of symmetry of the graph of a quadratic function f ( x)  ax 2  bx  c is
given by x  
b
. The vertex is
2a
 b
 b 
  , f     .
 2a  2a  
 b  b 2  4ac
.
2a
2
The standard form of a quadratic function is f ( x)  a x  h   k .
The solutions of a quadratic equation, ax 2  bx  c  0 , are x 
EOO = every other odd, 1, 5, 9, 13, …
2.1 Quadratic Functions



Analyze graphs of quadratic functions.
Write quadratic functions in standard form and use the results to
sketch graphs of functions.
Find the minimum and maximum values of quadratic functions in
real-life applications.
2.1 Page 99: #1-5, 11, 13, 17, 19, 23, 25, 29, 31, 45-49 odd, 55, 57, 61a&61b
2.2 Polynomial Functions of Higher Degree


Use the leading coefficient test to determine end behavior of graphs
of polynomial functions.
Find and use zeros of polynomial functions as sketching aids.
2.2 Page Page 112: Vocab. check #1-2, 4 and Exercises #15-19 odd, 23-29 odd, 33, 43,
45, 51,55,59,63,65, 69-77 odd, 91
2.3
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Real Zeros of Polynomial Functions
Use synthetic division to divide polynomials by binomials of the form
(x-k).
Use the Remainder Theorem and Factor Theorem.
Use the Rational Zero Test to determine possible rational zeros of
polynomial functions.
2.3 Page 127: #15, 19, 21, 25, 35, 39, 43, 45, 49, 53, 55, 95, 105
2.4 Complex Numbers
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Use the imaginary unit i to write complex numbers.
Add, subtract, and multiply complex numbers.
Use complex conjugates to write the quotient of two complex
numbers in standard form.
Plot complex numbers in the complex plane.
2.4 Page 137: #1-13 EOO, 15-19 odd, 25-33 odd, 37, 41, 43, 47, 49, 64, 65-75 odd
If interested in fractals, read p. 136. Also, read #79 & 80 to see how complex numbers are used
with electrical circuits.
2.5 The Fundamental Theorem of Algebra
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Use the Fundamental Theorem of Algebra to determine the
number of zeros of a polynomial function.
Find all zeros of a polynomial function including complex zeros.
Find conjugate pairs of complex zeros.
Find zeros of polynomials by factoring.
2.5 Page 144: #1, 3, 11-31 EOO, 37, 39, 43, 47, 59, 63, 65
2.6



Rational Functions and Asymptotes
Find the domains of rational functions.
Find horizontal and vertical asymptotes of graphs of rational
functions.
Use rational functions to model and solve real-life problems.
2.6 Page 152: #1, 5, 7-12, 13-19 odd (table of values optional), 23-39 EOO, 43, 49, 51 and
part of Unit 2 Review Sheet
2.7 Graphs of Rational Functions
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
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Analyze and sketch graphs of rational functions.
Sketch graphs of rational functions that have slant asymptotes.
Use rational functions to model and solve real-life problems.
2.7 Page 161: #9-33 EOO, 43, 45, 59, 61, 79, 83, 89, 91 and part of Unit 2 Review Sheet
2.8 Quadratic Models
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Classify scatter plots.
Use scatter plots and a graphing utility to find quadratic models
for data.
Choose a model that best fits a set of data.
2.8 Page 169: #1-9 odd, 15 and part of Unit 2 Review Sheet