1. 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

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

3. 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)

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

5. 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

6. 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 and
revenue of R(x) = - x2 +180x (both in dollars).
Determine the production level that would maximize profit.

7. 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?

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

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

10. 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) = x – x2. Determine how much of the product must be sold in order to break even.

11. 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?

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

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

14. 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?

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

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