Learning Resources
Outcomes
In this lesson you will
- find the x-intercepts or roots of the quadratic equation by a variety of methods including graphing, tables of values, guessing and checking, factoring, and completing the square
- use quadratic equations to solve problems involving the parabolic path of objects
By the end of this section students will be able to:
- derive and apply the quadratic formula
- analyze the quadratic formula to connect its components to the graphs of quadratic functions
- solve quadratic equations
- relate the nature of the roots of quadratic equations and the x- intercepts of the graphs of 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
Introduction
Mathematical Modeling, Book 3 p. 41 - 60
Having completed Section 1.3 , you how realize that some quadratic equations have x-intercepts, either one or two, or none. This means that at these points the y-value is 0 or 
. We call these values for x the roots of the quadratic equation that has been graphed.
There are other methods to find the roots of a quadratic equation including factoring, completing the square and indeed a formula. These are the ideas you will investigate during the lessons of this section. By determining these roots you will be able to use quadratic equations to solve real-world problems. From the formula you will be able to determine the nature of the roots of a quadratic equation without having to actually find the roots
Further investigation of these roots will exhibit relationships between the coefficients of the variables of the general form of the quadratic equation and the sum and the product of the roots.
This section will provide some useful skills, enjoy it !
This section should take 6 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- using technology to graph the quadratic and find its x-intercepts
- factoring quadratic polynomials
- simplifying radical expressions