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Lesson 8

1. Lesson 8

1.5. Explore

Mathematics 20-2 M3 Lesson 8

Module 3: Quadratics


Explore
 

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While you’ve been working with the quadratic formula, you had to evaluate b2 − 4ac. “Example 2” on page 416 of the textbook noted that if b2 − 4ac was a perfect square, the associated quadratic function, y = ax2 + bx + c, could be factored. The expression b2 − 4ac, which is known as the discriminant, can tell you more about the associated quadratic function.

 

The following applet allows you to explore how values of the discriminant and the graph of a quadratic function are related.

 

Try This 1
 

Open to the Quadratic Function: Discriminant applet to explore how the discriminant is related to the number of x-intercepts.

 

 

This is a play button that opens Quadratic Function: Discriminant.

 

The applet has sliders to change the values of the constants (a, b, and c) in y = ax2 + bx + c. Notice the information given below the sliders. You should see the discriminant, b2 − 4ac, and its value of 12 when initial values of a = 1, b = 0, and c = −3 are used.

 

Move the b-slider or the c-slider. What happens to the discriminant? What happens to the x-intercepts?

 

Experiment with the sliders and notice the values of the discriminant when there

  • are two x-intercepts
  • is one x-intercept
  • are no x-intercepts
  1. What is the relationship between the value of the discriminant and the number of x-intercepts?

  2. How does each situation relate to the position of the vertex?

  3. Do your generalizations also hold true when the a-value is negative? Move the a-slider and see. What do you conclude?
Share 1


assignment

Submit your work for Share 1 to your teacher for marking.

 

Based on your observations from Try This 1, discuss the following questions with another student or appropriate partner.

  1. How can the value of the discriminant tell you whether there will be one, two, or zero x-intercepts? (3 marks)

  2. Does your answer depend on whether the value of a is negative or positive? Why or why not? (2 marks)

  3. Summarize your discussion by creating a general rule relating the value of the discriminant to the number of x-intercepts. (3 marks)

course folder Place a copy of your responses in your course folder for reference later in the course.