# 7.1 polynomial functions

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7.1 Polynomial Functions. Degree and Lead Coefficient End Behavior. Polynomial should be written in descending order. The polynomial is not in the correct order3x 3 + 2 – x 5 + 7x 2 + x Just move the terms around -x 5 + 3x 3 + 7x 2 + x + 2 Now it is in correct form. - PowerPoint PPT Presentation

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• 7.1 Polynomial FunctionsDegree and Lead CoefficientEnd Behavior

• Polynomial should be written in descending orderThe polynomial is not in the correct order3x3 + 2 x5 + 7x2 + x

Just move the terms around-x5 + 3x3 + 7x2 + x + 2Now it is in correct form

• When the polynomial is in the correct orderFinding the lead coefficient is the number in front of the first term-x5 + 3x3 + 7x2 + x + 2Lead coefficient is 1It degree is the highest degreeDegree 5Since it only has one variable, it is a Polynomial in One Variable

• Evaluate a PolynomialTo Evaluate replace the variable with a given value. f(x) = 3x2 3x + 1Let x = 4, 5, and 6

• Evaluate a PolynomialTo Evaluate replace the variable with a given value. f(x) = 3x2 3x + 1Let x = 4, 5, and 6

f(4) = 3(4)2 3(4) + 1 = 37 = 3(16) 12 + 1 = 48 12 + 1 = 36 + 1 = 37

• Evaluate a PolynomialTo Evaluate replace the variable with a given value. f(x) = 3x2 3x + 1Let x = 4, 5, and 6

f(4) = 3(4)2 3(4) + 1 = 37f(5) = 3(5)2 3(5) + 1 =

• Evaluate a PolynomialTo Evaluate replace the variable with a given value. f(x) = 3x2 3x + 1Let x = 4, 5, and 6

f(4) = 3(4)2 3(4) + 1 = 37f(5) = 3(5)2 3(5) + 1 = 61 = 3(25) 15 + 1 = 75 15 + 1 = 61

• Evaluate a PolynomialTo Evaluate replace the variable with a given value. f(x) = 3x2 3x + 1Let x = 4, 5, and 6

f(4) = 3(4)2 3(4) + 1 = 37f(5) = 3(5)2 3(5) + 1 = 61f(6) = 3(6)2 3(6) + 1 =

• Evaluate a PolynomialTo Evaluate replace the variable with a given value. f(x) = 3x2 3x + 1Let x = 4, 5, and 6

f(4) = 3(4)2 3(4) + 1 = 37f(5) = 3(5)2 3(5) + 1 = 61f(6) = 3(6)2 3(6) + 1 = 91 = 3(36) 18 + 1 = 91

• Find p(y3) if p(x) = 2x4 x3 + 3x

• Find p(y3) if p(x) = 2x4 x3 + 3xp(y3) = 2(y3)4 (y3)3 + 3(y3)

p(y3) = 2y12 y9 + 3y3

• Find b(2x 1) 3b(x) if b(m) = 2m2 + m - 1Do this problem in two partsb(2x 1) =

• Find b(2x 1) 3b(x) if b(m) = 2m2 + m - 1Do this problem in two partsb(2x 1) = 2(2x 1)2 + (2x -1) 1=2(2x 1)(2x 1) + (2x 1) 1=2(4x2 2x -2x + 1) + (2x -1) 1= 2(4x2 4x + 1) + (2x 1) -1= 8x2 8x + 2 + 2x -1 1= 8x2 - 6x

• Find b(2x 1) 3b(x) if b(m) = 2m2 + m - 1Do this problem in two partsb(2x 1) = 8x2 - 6x

-3b(x) = -3(2x2 + x 1) = -6x2 3x + 3

b(2x 1) 3b(x) = (8x2 6x) + (-6x2 3x + 3)= 2x2 9x + 3

• End Behavior We understand the end behavior of a quadratic equation. y = ax2 + bx + cboth sides go up if a> 0 both sides go down a < 0

If the degree is an even number it will always be the same. y = 6x8 5x3 + 2x 5go up since 6>0 and 8 the degree is even

• End Behavior If the degree is an odd number it will always be in different directions. y = 6x7 5x3 + 2x 5

Since 6>0 and 7 the degree is oddraises up as x goes to positive infinite and falls down as x goes to negative infinite.

• End Behavior If the degree is an odd number it will always be in different directions. y = -6x7 5x3 + 2x 5

Since -6

• End Behavior If a is positive and degree is even, then the polynomial raises up on both ends (smiles)

If a is negative and degree is even, then the polynomial falls on both ends (frowns)

• End Behavior If a is positive and degree is odd, then the polynomial raises up as x becomes larger, and falls as x becomes smaller

If a is negative and degree is odd, then the polynomial falls as x becomes larger, and rasies as x becomes smaller

• Tell me if a is positive or negative and if the degree is even or odd

• Tell me if a is positive or negative and if the degree is even or odda is positive and the degree is odd

• Tell me if a is positive or negative and if the degree is even or odd

• Tell me if a is positive or negative and if the degree is even or odda is positive and the degree is even

• Tell me if a is positive or negative and if the degree is even or odd

• Tell me if a is positive or negative and if the degree is even or odda is negative and the degree is odd

• HomeworkPage 350 351#17 27 odd, 31, 34, 37, 39 43 odd

• HomeworkPage 350 351#16 28 even, 30, 35, 40 44 even