Learning Resources

Outcomes

In this lesson you will

• Explore the common differences in power sequences.
• Discover that a quadratic sequence of the form y = ax² + bx + c produces a sequence of common or constant differences at the second level.
• Discover that other power sequences produce a sequence of common differences at a higher level.
• Explore the relationship between the coefficient, a, and the second-level common difference in a quadratic sequence generated by the function
  y = ax² + bx + c
• Compare the graphs of quadratic and cubic sequences to note similarities and differences

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

• Demonstrate an understanding of patterns that are arithmetic, power, and geometric, and relate them to corresponding functions.
• Analyze tables and graphs to distinguish between linear, quadratic, and exponential relationships.
• Sketch graphs from descriptions, tables, and collected data.

Prerequisites

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

• The definitions and distinguishing characteristics of linear and quadratic functions.
• How to use symbols to represent linear and quadratic functions.
• How to use technology to graph linear and non-linear functions and find the equation of the curve of best fit.