1. Lesson 1

1.6. Discover 3

Mathematics 20-2 M3 Lesson 1

Module 3: Quadratics

 

Did You Know?


This photo shows a car headlight.

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The shape of the reflector inside flashlights and automobile headlamps is a parabola. This shape, formed by a quadratic function, reflects the light out in a concentrated forward beam instead of just a scattered pattern.

 



standard form of a quadratic function: a quadratic function written in the form y = ax2 + bx + c, where a ≠ 0

A quadratic function can be written in the form y = ax2 + bx + c. This is known as the standard form of a quadratic function.

 

What information does the standard form of a quadratic function tell you about the shape of the graph? How do the coefficients (a and b) and the constant (c) relate to the graph of a quadratic function?

 

Try This 1
 

Use Quadratic Functions to see what happens to the graph as you change the values of a, b, and c.

 

 

This is a screenshot for Quadratic Functions.

Screenshot reprinted with permission of ExploreLearning.

 



Once you have tried different combinations of values for the coefficients and constant, use the following questions to guide your investigation.

  1. Begin by exploring the effect of different coefficient values on linear functions. Set the value of a to zero.

    1. What type of function do you have? Answer

    2. With a set to zero, change the value of b. How does this affect the graph of the linear function? Be sure to try both positive and negative values for b. Answer

    3. With a set to zero, change the value of c. How does this affect the graph of the linear function? Make sure you try both positive and negative values for c. Answer
  1. Now explore the effect of different coefficient values on quadratic functions. Set the value of b and c to zero or leave at a constant value—that is, don’t change b and c. Change the value of a. What effect does changing the value of a have on the graph of a quadratic function? Try both positive and negative values for a. Remember that a ≠ 0 or you will have a linear function. Answer
  1. Set the value of c to zero. Set the value of a to 2. Change the value of b. Now set the value of a to −2 and repeat.

    1. What effect does changing the value of b have on the graph of a quadratic function when a is positive? Answer

    2. What effect does changing the value of b have on the graph of a quadratic function when a is negative? Answer

    3. What effect does changing the value of b have on the location of the parabola’s line of symmetry? Answer

      line of symmetry: a line about which a figure is symmetrical

       

      If a figure can be folded such that the two parts exactly match, the fold line would be a line of symmetry.

       

      This is a graphic showing the line of symmetry of a parabola.

       



  1. Leave the value of a and b constant. Remember that a ≠ 0 or you will not have a quadratic relation. Change the value of c.

    1. What effect does changing the value of c have on the graph of a quadratic function? Answer

    2. What part of the graph can be determined by c? Answer
  1. Leave the value of c constant. Change the values of a and b. What effect does this have on the y-intercept? Answer