Lesson 8

Recall from the Course Introduction that you will be creating your own course glossary. Open the Glossary Terms document that you saved to your course folder, and add in any new terms. It is suggested that you add the following new terms to your Glossary Terms document:

• discriminant
• quadratic formula

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Self-Check 2

Complete “Check Your Understanding” questions 1.a., 1.b., 2.c., 2.d., 3.c., and 3.d. on page 419 of the textbook to practise using the quadratic formula before moving on in this lesson. You might want to compare your answers to the answers provided after responding to each question. Answer

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Solving quadratic equations can be used in many problem situations. Watch the piece titled Flying Snowboard.

 

 

Self-Check 3

 

A snowboarder takes a jump and lands down the slope. His approximate height above the landing is h = −5x2 + 3x + 3.6, where x represents time in seconds.

1. Calculate the discriminant and identify how many roots there will be. Answer

2. How long was the snowboarder in the air? Answer

3. What is the maximum height during the jump? Round your answer to two decimal places. (You might like to use the Quadratic Function: Discriminant applet from the Explore section to complete part of this solution). Answer

Self-Check 4

1. An outdoor clothing retailer is overstocked with one style of snowboarding jacket. In order to sell more of the jackezts, the store has decided to discount the price. The marketing manager has figured out a quadratic function describing the net amount of profit, P, the store will earn from the sales.
   
   The function is P = −30x2 + 350x + 5000. In this function, x represents the number of successive $5 discounts to the price.

2. Assume you own 30 apartment units. When the rent is $800 per month, all the apartments are occupied. For each rent increase of $40 per month, one of the units becomes unoccupied.
   
   The following function relates the price increase, p, to the revenue, r.
   
   
    
   
   
   What rent should you charge to ensure you earn $25 000? Answer

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Look at the “Frequently Asked Questions” on page 423 of the textbook.

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If you haven’t done so already, you may want to add what you’ve learned about the quadratic formula and the discriminant to your notes organizer.

 

If you feel you need a bit more practice, complete Self-Check 5 before moving to Connect.

 

Self-Check 5

Complete all or parts of questions 2, 3, 7, and 8 on pages 419 and 420 of the textbook. When you finish a question, check your work using the shortened answers given on page 564 of the textbook. If you are still unclear about how to answer some questions, ask your teacher for help.