1.11 Solving Quadratic Word Problems given the equation Date: ______________________ Learning Goal: I can… use different types of quadratic equations provided to solve various quadratic word problems Solving W ord Problem Tips:
My own strategies: Other Strategies: Parabolas are commonly used to model certain types of situations: 1. Profit Axis of Symmetry: Optimal Value: Zeroes: Y-‐intercept: *Not all profits are attainable. 2. Height Axis of Symmetry: Vertex: Zeroes: Y-‐intercept: *Not all heights are attainable. *If the graph is height versus time, do not confuse the shape of the graph with the trajectory of the object. For example, the graph above could represent the graph of an object thrown straight up into the air. Examples 1. The population of a Canadian city is modeled by P(t ) = 12t 2 + 800t + 40000 , where t is the time in years since 2007. a) What will the population be in 2020? b) In what year is the population predicted to be 30000? 2. A construction worker repairing a window tosses a tool to his partner across the street. The height of the tool 2
above the ground is modelled by the quadratic function h(t ) = −5t + 20t + 25 , where h (t ) is height above ground in metres and t is the time in seconds after the toss. a) How high above the ground is the window? b) If his partner misses the tool, when will it hit the ground? c) What is the maximum height of the tool? 3. The cost, C (v ), in dollars per hour of running a certain steamboat is modelled by the quadratic function C (v ) = 1.8v 2 − 14.4v + 156.5 , where v is the speed in kilometres per hour. At what speed should the boat travel to achieve the minimum cost? 4. Anthony owns a business that sells parts for electronic game systems. The profit function for his business can be 2
modelled by the equation P (n ) = −0.5(n − 8) + 8 , where n is the quantity sold, in hundreds, and P(n ) is the profit in thousands of dollars. How many parts must Anthony sell in order for his business to make a profit? Homework Practice: Page 307 #8,11 (already completed/re-‐try)