Learning Resources
Outcomes
In this lesson you will
- use technology to explore the effects of changing the coefficients a and c on the parabola of the general form of the quadratic
- write quadratic functions in both standard and general form
By the end of this section students will be able to:
- analyze and describe the characteristics of quadratic functions
- solve problems involving quadratic equations
- analyze scatter plots, and determine and apply the equations of best fit, using appropriate technology
- describe and translate between graphical, tabular, written, and symbolic representations of quadratic relationships
- demonstrate an understanding of the relationships that exist between arithmetic operations and the operations used when solving equations
- translate between different forms of quadratic equations
- describe and interpret domains and ranges using set notation
- demonstrate an understanding of how parameter changes affect the graphs of quadratic functions
Introduction
Mathematical Modeling, Book 3 p. 24 - 40
In this section, you will review and extend the properties of quadratic functions and their graphs that you studied in Level I (Mathematic 1204) and Level II (Mathematics 2205)
Previously the transformational form of the quadratic equation 
was emphasized; during the next lessons the other forms of the quadratic, the standard form 
and the general form 
, will be examined in detail. To be able to easily convert from one form to another is a necessary skill since each has its own unique advantages in the various situations. Basic algebra skills are necessary for these conversions and in particular the technique of completing the square for a trinomial is used to convert the general form to the standard form.
Be careful with your algebraic manipulations and this topic should be easy going!
This section should take 5 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- general form of the quadratic function
- transformational form of the quadratic function
- effects of the coefficients on the shape of a graph (parabola) of a quadratic function
- characteristics of the graph of a quadratic function viz: vertex, axis of symmetry. maximum/minimum point, mapping rule for quadratics