Learning Resources

Outcomes

In this lesson you will

• Explore y = a(x - h)² + k,  a ¹ 0  which is known as the standard form for writing a quadratic function.
• Explore   y = ax² + bx + c,  a ¹ 0  which is known as the general form for writing a quadratic function.
• Explore how the general and standard forms are alike and how different.
• Explore what the values of a and c in the general form tell about the function and its graph.
• Revisit graphing parabolas and be introduced to the common terms used to describe parabolas.

By the end of this section you should 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 for curves 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 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

In this section, you will review and extend the basic properties of quadratic functions and their graphs. In particular, you will learn to work with quadratic functions other than in the transformational form, .  You will investigate the standard form of a quadratic function  and the general form of a quadratic function ,and explore the connection between these forms.

Following these activities, you will transform quadratic functions into perfect squares by completing the square. This technique of completing the square is used to transform the general form of a quadratic into the transformational form which you can use to identify the properties of the parabola.

The section concludes with an activity that enables you to determine a quadratic function when given the vertex and at least one other point on the parabola.

This section should take you about 5 hours to complete.

Prerequisites

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

• The general form of a quadratic function.
• The effects of the coefficients on the shape of the graph (parabola) of a quadratic function.
• The vertex of a parabola.
• The concept of maximum and minimum values of a quadratic function.
• How to write relationships using mapping notation.