mcf3m test #3 factoring and solving quadratic functions

MCF3M Test #3 – Factoring and Solving Quadratic Functions Name: ______________

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T A C K Total

12 18 12 38 80

Instructions:

1. Read each question carefully before answering. 2. Express all fractions in lowest terms. 3. Calculators can be used but cannot be shared. 4. Good Luck !!

Part 1: Knowledge and Understanding (K):

1. For the function f(x) = (x – 3) (x + 1) determine the following information. a) the zeros (1 mark) b) the equation for the axis of symmetry (1 mark) c) the coordinates of the vertex (2 marks) d) the direction of opening (1 mark)

2. Express the function f(x) = - (x + 4)(2x – 2) in standard form. State the value of the y-intercept. (4 marks)

3. Express the function f(x) = (x + 2)2 +5 in standard form. State the value of the y-intercept. (4 marks)

Test Score Parent/Guardian Signature


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4. Factor the following fully. (17 marks) a) 64x2 – 36 b) 15x2 + 3x – 12

c) -2x2 – 12x + 32 d) x2 + 19x + 70

e) 9x2 + 42x + 49 f) k3 – 16k

5. Determine the zeros for the following quadratic equations. Show your work. (8 marks) a) x2 – 10x = 0 b) x2 –x – 6 = 0


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Part 2: Communication (C):

6. Identify the 3 forms used to express quadratic functions and explain what information each form can tell you about its graph. Use examples to help support your answers. Organize the information in a table or other graphic organizer of your choice. (6 marks)

7. List the steps you would take to solve a quadratic equation. (4 marks)

8. Explain what is meant by an “inadmissible solution.” In what type of situation can this occur? (2 marks)


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Part 3: Application (A) :

9. A rectangular enclosure has an area in square metres given by 22 36A w w � � , where w is the width of the rectangle in metres. What is the maximum area of the enclosure? (4 marks)

10. A rock is thrown from the top of a cliff. The height of the rock above the ground is given by the function h(t) = -3t2 + 9t +30, where h(t) is the height of the rock above the ground, in metres, and t is the time in seconds. a) How tall is the cliff? Explain. (1 mark)

b) How long does it take the rock to reach the ground? (4 marks)

c) How is the rock being thrown off the cliff? Up into the air, sideways, or straight down? Justify and explain your answer (show a calculation to prove your answer). (3 marks)


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11. A golf ball is hit in to the air and its height is given by the function h(t) = 20t – 5t2, where h is the height and meters and t is the time in seconds. How long after it is hit is the golf ball at a height of 15 meters? Hint: If h(t) = 15, then what is t? Are both answers admissible? Why or why not?(6 marks)

Part 4: Thinking (T):

12. Mr. Neave jumps out of an airplane 4.4 km above the ground. The equation 24400 4H t � is an approximate model for Mr. Neave’s altitude in metres at t seconds after jumping out of the plane. a) If Mr. Neave opens his chute at an altitude of 1000m how long did he free fall? (2 marks) b) If the parachute does not open at 1000m, how much time is left to use the emergency

chute? Suprisingly all of his students are hoping that the chute opens !! (2 marks)


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13. Soundz Inc. makes MP3 players. The company’s profit is modelled by the equation 28 96 216P x x � � � , where P is the profit in hundreds of thousands of dollars and x is the number

of MP3 players made, in hundreds of thousands. a) How many MP3 players does the company have to make in order to break even? (4 marks) b) What is the maximum profit that the company can make and how many MP3 players do they

have to make in order to make this profit? (4 marks)

mcf3m test #3 factoring and solving quadratic functions

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