1. Lesson 4

1.1. Discover

Mathematics 20-1 Module 3

Module 3: Quadratic Functions

 

Discover
 

From studying the vertex form in Lessons 1 and 2, you know that the parameter a influences the parabolic graph’s direction of opening (upwards or downwards) and the width of the curve.

 

Parameter a is also found in the standard from of the quadratic function. How do the other parameters in the standard form, b and c, influence the characteristics of the curve?

 

Try This 1

 

Use Quadratics in Polynomial Form - Activity B to graph the functions in the two charts below. hint In order for this application to function properly, sign into LearnAlberta.ca first and then click on the play button provided below.

 

This is a play button that opens Quadratics in Polynomial Form - Activity B.

Screenshot reprinted with permission of ExploreLearning.

In Part A you will examine the effect of changing the value of b. In Part B you will examine the effect changing c has on the graph. Record your observations in charts like the ones shown. The charts will help you view emerging patterns.

 



Part A

  1. Complete a chart like the one shown and observe the effect of b on the parabola.

     
    Equation a b c Vertex y-Intercept Graph
    y = −1x2 + (−3)x − 1            
    y = −1x2 + (3)x − 1            
    y = −1x2 + (1)x − 1            
    y = −1x2 + (−1)x − 1            
    y = −2x2 + (−1)x − 1            


  2. Do you see any significant pattern? If you think you may have a generalization, try several other values for b to see if your generalization seems to be correct.

Part B

  1. Complete a chart like the one shown and observe the effect of c on the parabola.

     
    Equation a b c Vertex y-Intercept Graph
    y = −1x2 + (−3)x − 3            
    y = −1x2 + (−3)x − 2            
    y = −1x2 + (−3)x + 1            
    y = −1x2 + (−3)x + 3            


  2. Do you see any significant pattern? If you think you may have a generalization, try several other values for c and observe if your generalization seems to be correct.

course folder Save your responses in your course folder.

 

Share 1

 

Share your observations and generalizations about the effect of changing the value of b and c with a classmate. Be sure to address how the graph of the quadratic function is affected by a change in the value of b or c.

 

course folder Save your responses in your course folder.

Try these hints when using Quadratics in Polynomial Form - Activity B:

  • The “copy graph to clipboard” button can be used to capture the graph and record it in your chart.
  • Select the “show vertex/intercept data” to easily observe this information.