Warm-Up 2/201.
D
Rigor:You will learn how to analyze and graph
equations of polynomial functions.
Relevance:You will be able to use graphs and equations of
polynomial functions to solve real world problems.
2-2 Polynomial Functions
Example 1: Graph each function.
f(x) is similar to and is translated right 2 units.
g(x) is similar to and is reflected in the x-axis and translated up 1 unit.
Example 2: Describe the end behavior.
a. Degree is 4.Leading Coefficient is 3.and
b. Degree is 7.Leading Coefficient is β 2.and
c. Degree is 3.Leading Coefficient is 1.and
Example 3: State the number of possible real zeros and turning points of . Then determine all of the real zeros by factoring.
π₯3β5 π₯2+6 π₯=0
Degree is 3.f has at most 3 distinct real zeros.
f has at most 2 turning points.
π₯ (π₯2β 5π₯+6 )=0π₯ (π₯β 2 ) (π₯β 3 )=0f has real zeros at x = 0, 2, and 3.
Example 4: State the number of possible real zeros and turning points of . Then determine all of the real zeros by factoring.
π₯4 β3 π₯2β 4=0
Degree is 4.g has at most 4 distinct real zeros.
g has at most 3 turning points.
(π₯2 )2 β3 (π₯2 ) β 4=0
π’2 β3π’β 4=0
g has real zeros at x = β 2 and 2.
(π’+1)(π’β 4)=0(π₯2+1)(π₯2β 4 )=0
or
π₯2=β1π₯=Β±ββ1
π₯2=4π₯=Β± 2
Let
Example 5: State the number of possible real zeros and turning points of . Then determine all of the real zeros by factoring.
βπ₯4 βπ₯3+2 π₯2=0
Degree is 4.h has at most 4 distinct real zeros.
h has at most 3 turning points.
βπ₯2 (π₯2+π₯β 2 )=0
h has real zeros at x = 0, 1 and β2. The zero at 0 has a multiplicity of 2.
βπ₯2(π₯β1)(π₯+2)=0 or or
π₯=0 π₯=1 π₯=β2π₯=0
Example 6:
π₯ (2π₯+3)(π₯β 1)2=0
a. Degree is 4. f has at most 4 distinct real zeros and at most 3 turning points.
b. f has real zeros at x = 0, and 1. The zero at 1 has a multiplicity of 2.
π₯=0 π₯=1π₯=1π₯=β32
c. d.
ββ1math!
2-2 Assignment: TX p104, 4-40 EOE
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