Unit 1 Test: Quadratics 1. Convert from factored form to standard form: (5 marks) a) y = (x 2)(x + 6) b) y = 5(x + 2)(x + 6) 2. Convert from standard from to factored form: (2 marks each) a) 2 15 2 y = x + x b) 10 16 2 y = x x + c) 3 24 45 2 y = x + x + 3. Convert from vertex form to standard form: (3 marks) ( 2) 3 2 y = x + + 4. a) What are the roots of the following equation ( ) 2 y = x + 3 ? (1 mark) b) What is the vertex of the following equation? (1 mark) c) Explain why this equation is both in vertex form and in factored form. (2 marks) 5. A model rocket is equipped with a motion detector that measures the height of the rocket at 30 second intervals. On a recent flight, the detector recorded the following data. Time (s) Height (m) 0 0 30 315 60 540 90 675 120 720 150 675 180 540 210 315 240 0 a) Graph the data. (3 marks) b) Is the graph a parabola? (1 mark) c) When does the rocket reach its maximum height? (1 mark) d) What is the maximum height? (1 mark) e) When does the rocket land? (1 mark) 6. State the transformations of the following and sketch the graph. (5 marks) 2( 3) 6 2 y = x + 7. The population of a city in Ontario can be modelled by the following equation: 6 120 3000 2 P = x + x + or 6( 10) 2400 2 P = x + + , where t represents the time in years and P represents the population. When t=0, the year is 2000. a) What was the population in the year 2000? (1 mark) b) What year is the population at its lowest point? What is the population during this time? (1 mark) c) Which equation is more helpful to answer a)? Why? (2 marks) d) Which equation is more helpful to answer b)? Why? (2 marks) 8. A model rocket is launched from an elevated pad. Its flight path through the air is modelled by h = -5t2 - 10t + 40, for h the height of the rocket in metres and t the time in seconds. a) When does the rocket land? (Hint: Looking for factored form). (3 marks) b) How high was the rocket when it was launched? (1 mark) c) Graph the data using time increments of 1 second. (3 marks) d) What is the maximum height of the rocket? (1 mark