MHF 400 Polynomial Functions: Thinking Task Provide full algebraic solutions for any TWO questions. 1. Determine the equation for a cubic function that has the following characteristics: End behaviour as x, y and as x o, y There are three x-intercepts; two are located at x = -6 and x=0.5, the other is unknown The function contains the points (2, 24) and (-4, 9) 2. The remainder when f(x) = x - 2x + ax - x + bx - 2 is divided by x + 1 is -7. When f(x) is divided by x - 2, the remainder is 32. Determine the remainder when f(x) is divided by x - 1 www 3. Two fighter jets are flying practice maneuvers. The height, in hundreds of feet, above the ground of the first jet is given by f(x) = 4x* 3x + 5x 21x + 10, and the height of the second one is given by g(x) = 4x* 2x a) Find the times when the two jets are at the same height. 7x + 20x - 20, where x is the time in minutes from noon. b) State the time intervals for which the first jet f(x) is higher than the second jet g(x) 4. Factor Trees :The bottom row of this factor tree, shows all of the prime factors of 48. If we were to take the product of any of these prime factors, the product would also be a factor of 48. 48 1 3 16 For example: 3x2=6 2x2x2=8 Six is a factor of 48 Twelve is factor of 48 4 Use your knowledge of factors and the Factor Theorem to prove that 3 2 2 6x + 3x + 10 is divisible by x - x - 2. - Level 4 Level 3 Level 2 . Answers are clearly, concisely, and accurately constructed and effectively supported through algebraic justification. Answers are mostly accurately constructed and have some justification. Answers are clearly and accurately constructed and supported through good algebraic justification. . A conjecture is made, applied, and validated. Answers show a good degree of understanding . A conjecture is made, applied, and somewhat validated. . A suitable conjecture is made, applied, and validated. . Answers show satisfactory degree of understanding Answers show a high degree of understanding X 4 3 2 2 x x 2 x 2 x 2 + 3 x 2 x 2 2 2 Level 1 Answers are constructed inaccurately with some explanation. An inaccurate conjecture is made, applied, and somewhat explained. Answers show a limited degree of understanding 4242 Level R Criteria Not Met