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Students should be able to…
› Evaluate a polynomial function.
› Graph a polynomial function.
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Section 6.1 Page 326 – 327 # 16 – 49 every 3, 50
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is a function is in the form
f(x) = anxn + an-1xn-1 + an-2xn-2 + … + a1x1 + a0
All the coefficients are real numbers (not imaginary)
Exponents are whole numbers (positive integers) an is the leading coefficient n is the degree of the polynomial a0 is the constant term
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0
1
2
3
4
Constant
Linear
Quadratic
Cubic
Quartic
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Is it a polynomial? Is the polynomial in standard form? What is the degree of the polynomial What is the leading coefficient of the polynomial? What is the constant(y-intercept) of the polynomial?
a. f(x) = 3x2 + 3x3 – 4x5 + x – 6
b. f(x) = 4x3 – 14x -2 + x – 6
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Examples:1. f(x) = 3x5 – x4 – 5x + 10 Find f(–2)
2. f(x) = –3x3 + 4x2 + 2x Find f(–3)
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a) f(x) = 3x5 – x4 – 5x + 10, find f(–2)
–2 3 –1 0 0 –5 10
3
-6
-7
14
14
-28
-28
56
51
-102
-92
+
Step 1: Write the polynomial in standard form, if not already.Step 2: Write the coefficients of x as shown below and use synthetic substitution.
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b) f(x) = –3x3 + 4x2 + 2x, find f(4)
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Degree Leading Coefficient
Left-hand Behavior
Right-hand Behavior Picture
Even Positive
Even Negative
Odd Positive
Odd Negative
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a) f(x) = -x3
What is the degree?
What is the leading coefficient?
Describe the end behavior
3 (odd)
-1 (negative)
Up on left, Down on right
Make a table and graph.
xfx
xfx
, as and
, As
x –2 –1 0 1 2
y
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b) f(x) = x4 – 2x – 3
What is the degree?
What is the leading coefficient?
Describe the end behavior.
4 (even)
1 (positive)
Up on left, Up on right
Make a table and graph.
xfx
xfx
, as and
, As
x –2 –1 0 1 2
y
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Section 6.2Page 333 - 335 #16 – 46 every 3, 49 – 52 all, 53 – 71 every 3