1. Lesson 3

1.8. Explore 4

Mathematics 20-1 Module 3

Module 3: Quadratic Functions

 

Did You Know?

Today in the shot put event, elite athletes throw the shot much farther than anyone ever could when world records were first established. Training techniques and increased understanding of the physics and biophysics involved have enabled huge gains.

 

Men throw a 7.27-kg shot and women throw a 4-kg shot. Here are some interesting statistics:

 

 
  Year Athlete Country Distance (m)
Female 1924 Violette Gouraud-Morris Paris, France 10.15
1987 Natalya Lisovskaya Moscow, USSR 22.63
Male 1909 Ralph Rose San Francisco, USA 15.54
1987 Randy Barnes Los Angeles, USA 22.63

 

Dylan Armstrong from Kamloops, British Columbia, holds the Canadian shot put record of 21.58 m.



Self-Check 2

 

This is an image of a man preparing to throw a shot put.

Black 100/Photodisc/Thinkstock

 

The path of a shot put can be closely approximated by a quadratic function. Assume that a super-athlete starts to throw the shot from a height of 1.6 m. The standard form of the quadratic function describing the parabolic path is y = −0.0445x2 + 0.09434x + 1.6. The output distances will be in metres.

  1. Convert the quadratic function for the shot put from standard form to vertex form. Answer

  2. How high will the shot go? Answer

  3. How far from the thrower will the maximum height be? Answer

  4. Complete a graph to check your results using a graphing calculator, graphing program, or graph paper. Graph both forms of the function to verify that your conversion was accurate. hint Answer

  5. From the graph, explain approximately how far from the thrower the shot will land. Answer

If you feel you have a solid understanding of how to convert a quadratic equation in standard form to the vertex form, go to Connect. If you need a bit more practice, complete Self-Check 3.



textbook
Self-Check 3

 

Complete questions 3, 9, 12, 14, and 16 on pages 193 to 195 in the textbook. Check your work in the back of the textbook. If you are still unclear about how to answer some questions, contact your teacher.


formula
Add the standard and vertex forms of quadratic equations to your copy of Formula Sheet.
You may need to adjust your window settings to see the parabola on your calculator window. One quick method to start the window adjustment is to use zoom, and then select “zoomfit.”