 Students should be able to… › Evaluate a polynomial function. › Graph a polynomial function.

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Presentation transcript:

 Students should be able to… › Evaluate a polynomial function. › Graph a polynomial function.

 Section 6.1  Page 326 – 327 # 16 – 49 every 3, 50

is a function is in the form f(x) = a n x n + a n-1 x n-1 + a n-2 x n-2 + … + a 1 x 1 + a 0  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  a 0 is the constant term

00 11 22 33 44  Constant  Linear  Quadratic  Cubic  Quartic

 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) = 3x 2 + 3x 3 – 4x 5 + x – 6 b. f(x) = 4x 3 – 14x -2 + x – 6

Examples: 1. f(x) = 3x 5 – x 4 – 5x + 10 Find f(–2) 2. f(x) = –3x 3 + 4x 2 + 2x Find f(–3)

a) f(x) = 3x 5 – x 4 – 5x + 10, find f(–2) –23–100– 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.

b) f(x) = –3x 3 + 4x 2 + 2x, find f(4)

DegreeLeading Coefficient Left-hand BehaviorRight-hand BehaviorPicture EvenPositive EvenNegative OddPositive OddNegative

a) f(x) = -x 3 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. x–2–1012 y

b) f(x) = x 4 – 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. x–2–1012 y

Section 6.2 Page #16 – 46 every 3, 49 – 52 all, 53 – 71 every 3