Unit 2: Quadratic Functions Minds On A highway overpass has a shape that can be modeled by the equation of a parabola. If the edge of the highway is the origin, and the highway is 10 m wide, what is the equation of the parabola? What information do we still need to determine its complete equation? The height of the overpass is 13 m at a distance of 2 m from the edge. T

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Learning Goals: I can solve realistic problems that involve quadratic functions

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Strategies for solving problems: Step One: Read the problem What information is given? Is any of the information irrelevant? What assumptions can you make? What are you being asked to find? What does it look like? (Diagram) What tools can you use to solve the problem? (Formulas)

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Strategies for solving problems: Step Two: Solve the problem Do the calculations

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Strategies for solving problems: Step Three: Check your answer Is your answer reasonable? Write a therefore statement

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Example: A company that manufactures x bicycles per day has costs of C(x)= 20x +1500 and revenue of R(x) = - x2 +180x (both in dollars). Determine the production level that would maximize profit.

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas What info do we have? What do you need to find? How can you find it?

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Solve - Calculations

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Check answer Therefore statement

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Example: The price consumers will pay for an item depends on the number available to sell (if there’s a lot of a product, it’s cheap. If a product is scarce, it’s expensive). We call this the “demand function.” For a particular product, this price can be modeled by P = 200 – 3x. The cost to produce an item is modeled by the equation C(x) = 75 + 80x – x2. Determine how much of the product must be sold in order to break even.

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas What info do we have? What do you need to find? How can you find it?

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Solve - Calculations

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Check answer Therefore statement

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Example: A ball is tossed upward into the air from the roof of a building. Its path is modeled by the equation h(t) = -16t2 + 40t + 50, where h is the height in feet, and t is the time in seconds. How tall is the building? B) When will the ball reach its maximum height, and what will that height be? C) When will the ball hit the ground?

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas

Unit 2: Quadratic Functions Lesson 7: Problem Solving with Parabolas Homework Worksheet