17 PreCalculus AP U6 Polynomials (MHF) Name:

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1 17 PreCalculus AP U6 Polynomials (MHF) Name: ASSIGNMENT Solve Polynomial Word Problems Solve x + 49x + 8x 12 = 2x x 30 = 8x 30x The distance of a ship from its harbour is modelled by the function d( t) = 3t + 3t + 18t where t is the time elapsed in hours since departure from the harbour. a) When does the ship return to the harbour? b) Draw a sketch of the function where 0 t 3 c) What do you need to find to determine the time that the ship begins its return trip back to the harbour. Use technology to verify that this point is NOT halfway between zeros. Thus the need to learn derivatives in calculus 17

2 18 PreCalculus AP U6 Polynomials (MHF) Name: 4. The width of a rectangular prism is wcentimeters. The height is 2 cm less than the width. The length is 4 cm more than the width. If the magnitude of the volume of the prism is 8times the measure of the length, what are the dimensions of the prism? 5. A rectangular piece of cardboard measuring 12 in by 8 in is made into an open box by cutting squares from the corners and turning up the sides. 3 If the volume of the box is 60 in, what are its dimensions? 18

3 19 PreCalculus AP U6 Polynomials (MHF) Name: 6. A cylinder with a radius of r and a height of h is 7. Three students share a birthday on the same day. inscribed (see pic) within a sphere that has a radius Quinn and Ralph are the same age, but Audrey is of 4 units. Derive a polynomial function V(h) in two years older. The product of their ages is standard form, that expresses the volume of the greater than the sum of their ages. How old is each cylinder as a function of its height. person. 19

4 20 PreCalculus AP U6 Polynomials (MHF) Name: ASSIGNMENT Regression With Technology 1. Create a scatter plot of the data set using technology. Find the best regression model for your data (with regression coefficient as close to 1 as you can get it) Record: Technology used Equation R 2 value TI-89 desmos excel Year Cost A certain business company spends money of advertising to get specific revenues back. The data is provided below. Advertising (in $ s) Revenue (in $ s) a. Use techology to determine the equation that best fits the data. b. What is the domain of this function for this real life situation? c. For what amount of advertising does the company get an absolute maximum in revenue? 20

5 21 PreCalculus AP U6 Polynomials (MHF) Name: ASSIGNMENT Recap Factoring & Inequalities Factor each expression completely

6 22 PreCalculus AP U6 Polynomials (MHF) Name: Solve the following inequalities, state the solution in interval notation Solve the following inequalities by sketching polynomials

7 23 PreCalculus AP U6 Polynomials (MHF) Name: ASSIGNMENT Imaginary Numbers and Complex Roots of Polynomials (AP) 1. Simplify the following into a + bi form a) 121 b) 36 9 c) d) ( 3 6 ) 2 e) 144 f) -i(2i) g) (2-5i)(7 + 2i) h) 7i 7 i) -2(3 - i) + 5(-2 + 3i) j) ( 1+ i 3) 3 k) 15 6i l) 45 25i 15i m) 2 + 3i 2 3i n) i o) Graph the answers to #1 f), g), h), i) on the complex plane (Argand diagram) p) 11-7i q) 17 i 8 23

8 24 PreCalculus AP U6 Polynomials (MHF) Name: 2. Find an equation of lowest degree with integral coefficients that has zeros 2i and Find the value of b if 1 3 i is a root of 2 x + bx 2b = 0 4. Find all complex roots. a) b) 5 24

9 25 PreCalculus AP U6 Polynomials (MHF) Name: ASSIGNMENT Absolute Values/Reciprocals/Roots with Polynomials (MHF+AP) Sketch Absolute Value of these graphs overtop of the given sketches State the equations of your sketch for questions # 1-3 (questions 2 and 3 don t show scale of y-axis so you can assume any vertical stretch factor or none at all) 6. State the equation for original graph #4 25

10 26 PreCalculus AP U6 Polynomials (MHF) Name: Sketch Reciprocals of these graphs overtop of the given sketches Sketch

11 27 PreCalculus AP U6 Polynomials (MHF) Name: For the following graphs a) State a family of equations that would describe the original given graphs b) Sketch Both EVEN and ODD Roots of these graphs, do it separately or use different colours

12 28 PreCalculus AP U6 Polynomials (MHF) Name: Match the following graphs to their equations. There are more choices for equations given, so think! A. B. C. D. E. F. G. H