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.