Unit 3 Day 3 Graphs of Polynomial Functions Name Pre-AP Calculus Hour Find a polynomial function that has the given zeros. 1) 0, -2, -3 2) 0, 2, 5 3) 4, - 3, 3, 0 4) -2, -2, 0, 1, 2 5) 1+ V3, 1-V3 6) 6 + V3, 6-V3 7) 2, 4 + 15, 4-15 8) 4, 2 + 17, 2- 17 Find all the zeros of the polynomial function. 9.) f (x) = x4 -4x2 10.) g(x) = x4 - 10x2 +9 Solve each equation using the quadratic formula and state the nature of the roots. 11.) 2x2 - 7x + 3 = 0 12.) 7x2 + 6x + 2 = 0Use the Leading Coefficient Test to determine the right-hand and left-hand behavior of the graph of the polynomial function. 13 . ) f (x ) = =x3 +5x 14.) g(x) = 1-x6 15.) f(x) = 2x3 - 3x2 - 12x + 2 16.) f(x) = x4 - 8x2 + x+16 17.) g(x) = -3x4+ 8x3 18.) g(x) = 8x5 - 5x4 - 20x3 For each function: a) Classify the exponent of the leading term as even or odd, and classify the coefficient of the leading term as positive or negative. b) Use the information from part (a) to describe the end behavior of the function. 19.) f(x) = -5x6 +4x5 +2x -3 20.) f (x) = -7x9 -2x+3 21.) g(x) = -3+2x+5x5 22.) g(x) = -7x+3+5x4 For exercises 23-26. the end behavior of a polynomial function is given. State whether the exponent of the leading term of each function is even or odd, and whether the coefficient of the leading term is positive or negative. As x - too, f(x) - -0o, As x - too, f(x) - too, 23.) As x - -0o, f(x) - too 24.) As x - -co, f(x) - too 25.) As x - too, f(x) - -0o, 26.) As x - too, f(x) - too , As x - -0o, f (x) - -00 As x - -0o , f ( x ) - -00Unit 3 Day 4 - Real Zeros of Polynomial Functions Name Pre-AP Calculus Hour Use long division to divide. 1) 2x2 + 10: + 12 : (2+3) 2) ( 423 - 7x2 -11x +5) : (4: +5) 3 ) (623 + 10x3 + x +8) : (212 + 1) 4) (2' + 3x2 + 1) : (12 -2x+3) 5) (23 -9) : (22 + 1 ) 6) (2:23 - 427 - 15x +5) : (2-1) Use synthetic division to divide. 7) (323 - 1727 + 15x -25) : (2-5) 8) (623 + 712 - 1 + 26 : (2-3) 9) (923 + 1827 + 16: + 32) : (2+2) 10 ) (23 + 512 : (2+8)11) ( 423 + 1623 -23x -15) 4 2+2 12) (323 - 427 +5 ) 4 2 - 2 Use the remainder theorem to find each function value. 13) f(x) = 423 -13x + 10 a) f(1) b) f(-2) Use the factor theorem to show that x is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. 14) x' - 7x+6 =0; x =2 15) 2x3 - 1523 + 27x -10 =0; a=- Use (a) Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of f. (b) list the possible rational zeros, and (c) determine all the zeros off. 16) f(x) =-2x*+13x-21x2+2x+8 17) f(x)=-3x'+20x2-36x+16 a) a) b) b) 18) f(x ) =4x4 -17x2 +4 a) b)