3.1 questions 2,4,5,7

3.2 questions 9,12,13

3.3 questions 14

7 . The main span of the suspension bridge over the Peace River in Dunvegan, Alberta, has supporting cables in the shape of a 3.2 Investigating Quadratic Functions in parabola . The distance between the towers Standard Form, pa m, pages 163-179 is 274 m. Suppose that the ends of the 9. For each graph, identify the vertex, axis of cables are attached to the tops of the two symmetry, maximum or minimum value, supporting towers at a height of 52 m direction of opening, domain and range, above the surface of the water, and the and any intercepts. lowest point of the cables is 30 m above a) the water's surface . a) Determine a quadratic function that represents the shape of the cables if the origin is at 4 2 0 8 i) the minimum point on the cables 12 ii) a point on the water's surface directly below the minimum point of the cables ifi) the base of the tower on the left b) b) Would the quadratic function change over the course of the year as the seasons change? Explain. 5 000 or N A -10 8 6 -4 -2 0 10. Show why each function fits the definition of a quadratic function. a) y = 7(x + 3)2 -41 8. A flea jumps from the ground to a height b) y = (2x + 7)(10 - 3x) of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin 11. a) Sketch the graph of the function is located at the point from which the flea f(x) = -2x2 + 3x + 5. Identify the vertex, the axis of symmetry, the jumped. Determine a quadratic function direction of opening, the maximum in vertex form to model the height of or minimum value, the domain and the flea compared to the horizontal range, and any intercepts. distance travelled. b) Explain how each feature can be Did You Know? identified from the graph. The average flea can pull 160 000 times its own mass and can jump 200 times its own length. This is equivalent to a human being pulling 24 million pounds and jumping nearly 1000 ft! Chapter 3 Review . MHR 199Elle 15. Without graphing, state the vertex, the axis 12. A goaltender kicks a soccer ball through of symmetry, the maximum or minimum the air to players downfield. The value, and the domain and range of the trajectory of the ball can be modelled by function f(x) = 4x2 - 10x + 3. the function h(d) = -0.032d2 + 1.6d, 16. Amy tried to convert the function where d is the horizontal distance, in y = -22x2 - 77x + 132 to vertex form. metres, from the person kicking the Amy's solution: ball and h is the height at that distance, y = -22x2 - 77x + 132 in metres . y = -22(x2 - 3.5x) + 132 a) Represent the function with a graph, showing all important characteristics. y = -22(x2 - 3.5x - 12.25 + 12.25) + 132 y = -22(x2 - 3.5x - 12.25) - 269.5 + 132 b) What is the maximum height of the y= -22(x - 3.5)2 -137.5 ball? How far downfield is the ball when it reaches that height? a) Identify, explain, and correct the errors. c) How far downfield does the ball hit b) Verify your correct solution in several the ground? different ways, both with and without technology. d) What are the domain and range in this situation? 17. The manager of a clothing company is 13. a) Write a function to represent the area analysing its costs, revenues, and profits of the rectangle. to plan for the upcoming year. Last year, a certain type of children's winter coat was priced at $40, and the company sold 10 000 of them. Market research says that 5x + 15 for every $2 decrease in the price, the manager can expect the company to sell 500 more coats. 31 - 2x a) Model the expected revenue b) Graph the function. as a function of the number of c) What do the x-intercepts represent in price decreases. this situation? b) Without graphing, determine the d) Does the function have a maximum maximum revenue and the price that value in this situation? Does it have will achieve that revenue. a minimum value? c) Graph the function to confirm your e) What information does the vertex give answer. about this situation? f) What are the domain and range? d) What does the y-intercept represent in this situation? What do the x-intercepts represent? 3.3 Completing the Square, pages 180-197 e) What are the domain and range in 14. Write each function in vertex form, and this situation? verify your answer. f) Explain some of the assumptions that a) y = x2 - 24x + 10 the manager is making in using this b) y = 5x2 + 40x - 27 function to model the expected revenu c) y = -2x2 + 8x d) y = -30x2 - 60x + 105 200 MHR . Chapter 3Elle Chapter 3 Review 5. Write a quadratic function in vertex form 3.1 Investigating Quadratic Functions in for each graph. Vertex Form, pages 142-162 a) 1. Use transformations to explain how the graph of each quadratic function IN compares to the graph of f(x) = x2. Identify the vertex, the axis of symmetry, -10 8 6 -4 2 0 / 2 the direction of opening, the maximum or minimum value, and the domain and range without graphing. a) f(x) = (x+6)2 - 14 b) f (x ) = -2x2 + 19 c) f ( x ) = =(x -10)2 + 100 b) d) f (x) = -6(x - 4)2 2. Sketch the graph of each quadratic function using transformations. Identify the vertex, the axis of symmetry, the maximum or minimum value, the domain -2 0 and range, and any intercepts. a) f(x) = 2(x + 1)2 - 8 b) f (x) = -0.5(x - 2)2 + 2 3. Is it possible to determine the number of x-intercepts in each case without graphing? Explain why or why not. 6. A parabolic trough is a solar-energy collector. a) y = -3(x - 5)2 + 20 It consists of a long mirror with a cross- b) a parabola with a domain of all real section in the shape of a parabola. It works numbers and a range of (y | y 2 0, y E R} by focusing the Sun's rays onto a central c) y = 9 + 3x2 axis running down the length of the trough. d) a parabola with a vertex at (-4, -6) Suppose a particular solar trough has width 180 cm and depth 56 cm. Determine the 4. Determine a quadratic function with each quadratic function that represents the cross- set of characteristics. sectional shape of the mirror. a) vertex at (0, 0), passing through the point (20, -150) b) vertex at (8, 0), passing through the point (2, 54) c) minimum value of 12 at x = -4 and y-intercept of 60 d) x-intercepts of 2 and 7 and maximum value of 25