Secondary Mathematics II [2011]
Back

Analyze functions using different representations.
For F.IF.7b, compare and contrast absolute value, step and piecewisedefined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range and usefulness when examining piecewise-defined functions. Note that this unit, and in particular in F.IF.8b, extends the work begun in Mathematics I on exponential functions with integer exponents. For F.IF.9, focus on expanding the types of functions considered to include, linear, exponential, and quadratic.

Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factored.

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Applications of Quadratic Functions video
This video introduces and explains the topic.
This lesson unit is intended to help educators assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation.
• Functions and Everyday Situations
This lesson unit is intended to help educators assess how well students are able to articulate verbally the relationships between variables arising in everyday contexts, translate between everyday situations and sketch graphs of relationships between variables, and interpret algebraic functions in terms of the contexts in which they arise. Students will also reflect on the domains of everyday functions and in particular whether they should be discrete or continuous.
• Functions and the Vertical Line Test
The vertical line test for functions is the focus of this lesson plan.
• GeoGebra
GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards.
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Intercepts of Linear Equations video
This video introduces the topic.
• Non-linear Functions video
This video introduces non-linear functions.
• Quadratic Functions and Modeling F.IF.7, F.IF.8 and F.IF.9 Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics II Cluster "Analyze Functions Using Different Representations" / Standards F.IF.7, F.IF.8 and F.IF.9
• Solve Quadratic Expressions by Factoring video
This video introduces and explains the concept.
• Solving Quadratic Equations by Completing the Square
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Quadratic Equations by Factoring
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Solving Quadratic Functions by Completing the Square video
This video introduces and explains the topic.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Office of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Office of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.