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.