Education Technology

### Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Functions

## International Baccalaureate: Discrimination of Parabolas

### Objectives

Understand the role of the discriminant using technology and algebraically. (ACMMM010)

### Vocabulary

Vertex, Turning Point, Discriminant, Conjecture

Students use an investigative problem solving approach to determine the role of the discriminant for quadratic functions. The discriminant is displayed on the screen and constantly updates as students translate and dilate the parabola. The investigation is scaffolded by initially limiting manipulations of the parabola to transformations where the coefficient of x-square is positive one. In the next stage this is changed to negative one then finally, it becomes a variable so students can dilate and transform the parabola. Students are required to constantly refine their conjecture(s) with regards to the function of the ‘special number’. The final question is an extension opportunity for students to use algebra to move their conjecture to a theorem.

This lesson involves exploring the formula for compound interest as a function of the initial deposit, interest rate, and the number of pay periods per year.

As a result, students will:

• Learn the relationship between the interest rate and the total amount in the account.
• Learn the relationship between the number of pay periods and the total amount in the account.
• Discover the limiting condition as the number of pay periods increases without bound.