A LGEBRA 2 5.3 Day 1 Polynomial Functions. R ECALL.
Transcript of A LGEBRA 2 5.3 Day 1 Polynomial Functions. R ECALL.
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ALGEBRA 25.3 Day 1
Polynomial Functions
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RECALL
A polynomial is an expression that is a sum of variables and exponents.
Degree Type Example0 Constant 121 Linear2 Quadratic3 Cubic4 Quartic
Degree n Examples vary
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LEADING COEFFICIENT
The coefficient of the first term of a polynomial in standard form is called the leading coefficient.
Example Leading coefficient12 12
45
8
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EXAMPLE 1
State the degree and leading coefficient of each polynomial in one variable. If it is not a polynomial in one variable, explain why.a) b)
c)
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REAL WORLD – EXAMPLE 2
RESPIRATION The volume of air in the lungs during a 5-second respiratory cycle can be modeled by v(t) = –0.037t
3 + 0.152t
2 + 0.173t, where v is the volume in liters and t is the time in seconds. This model is an example of a polynomial function. Find the volume of air in the lungs 1.5 seconds into the respiratory cycle.
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EXAMPLE 3
If , find .Step 1: Find
Step 2: Find
Step 3: Now subtract step 1 and 2.
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YOU TRY
Find g(2x + 1) – 2g(x) if g(b) = b2 + 3.
A. 1
B. 2x
2 + 4x – 2
C. 2x
2 + 4x + 10
D. 2x
2 – 2
Hint:Step 1: Find Step 2: Find Step 3: Now subtract step 1 and 2.
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EXIT SLIP
1. Determine whether 3x3 + 2x2 – 3 is a polynomial in one variable. If so, state the degree and leading coefficient.
2. Find if
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ALGEBRA 25.3 Day 2
Polynomial Functions
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Zeros of Even- and Odd-Degree Functions Odd-degree functions will always have an
odd number of real zeros. Even-degree functions will always have an
even number of real zeros or no zeros at all.
The number of turns is always one less than the degree.
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EXAMPLE 1For each graph, Describe the end behavior Determine whether it represents an odd-
degree or an even-degree polynomial function
State the number of real zerosa) b)
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YOU TRY
For the graph, determine whether it represents an odd-degree or an even-degree function, and state the number of real zeros.
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EXIT SLIPFor the graph, Describe the end behavior Determine whether it
represents an odd-degree or an even-degree polynomial function
State the number of real zeros