Learning Resources

Outcomes

In this lesson you will learn

• Investigate the relationship between the roots of a quadratic equation and the value of the discriminant from the quadratic formula.
• Explore how the transformational form can determine whether the graph of a quadratic function has two, one, or zero x-intercepts.

By the end of this section you should be able to:

• Derive and apply the quadratic formula.
• Solve quadratic equations.
• Relate the nature of the roots of quadratic equations and the x-intercepts of the graphs of the corresponding functions.
• Represent non-real roots of quadratic equations as complex numbers.
• Demonstrate an understanding of the role of irrational numbers in applications.
• Demonstrate an understanding of the nature of the roots of quadratic equations.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• The quadratic formula.
• The meaning of the zeros of a function.
• How to change between the various forms (general, standard, transformational) of the quadratic function.