Quadratics, #1-The Graph
Part of Curriculum Unit:The Quadratic Function, an Introduction
Abstract help
Students will use a graphing technology to view the graphs
of quadratic functions that are ordered from f(x)=ax2 to
f(x)=ax2+c to f(x)=ax2+bx+c.
They should be provided with graph paper or a printout of the
worksheet and instructed to make sketches of the graphs they see.
Student response should be elicited to questions:
What affect does changing the parameter a have on the graph?
What affect does changing the parameter c have on the graph?
And the more difficult question...What affect does b have on the graph?
A large group discussion, either teacher led or built around group presentations should summarize the affects of the parameters.
of quadratic functions that are ordered from f(x)=ax2 to
f(x)=ax2+c to f(x)=ax2+bx+c.
They should be provided with graph paper or a printout of the
worksheet and instructed to make sketches of the graphs they see.
Student response should be elicited to questions:
What affect does changing the parameter a have on the graph?
What affect does changing the parameter c have on the graph?
And the more difficult question...What affect does b have on the graph?
A large group discussion, either teacher led or built around group presentations should summarize the affects of the parameters.
National Standards help
Understand various types of patterns and functional relationships
By observing similarities in the graphs of all functions of the form f(x)=ax2+bx+c, a not 0.
Extend mathematical knowledge by considering the thinking and strategies of others
By discussing conclusions about parameters with classmates.
By observing similarities in the graphs of all functions of the form f(x)=ax2+bx+c, a not 0.
Extend mathematical knowledge by considering the thinking and strategies of others
By discussing conclusions about parameters with classmates.
Pre-requisite Skills help
Students who undertake this activity will have had prior experience which includes plotting points on a coordinate system, observing a graph pattern related to a function type (linear) and defining exponents - at least exponents included in the natural number system.
Students should also be familiar with the use of some graphing tool.
Students should have experience or be trained for cooperating in groups to discuss experiences and agree on a final report product.
Students should also be familiar with the use of some graphing tool.
Students should have experience or be trained for cooperating in groups to discuss experiences and agree on a final report product.
Teacher Information help
Activities are designed to be used with a graphing utility.
An introduction to the activity should include directions for the student to:
Make a "good" but not necessarily point-perfect sketch of the graphs.
To think about the relation between the parameters and the graph as they are working through the examples.
In some way, students should be introduced to vocabulary (parabola, symmetry, parameter, y-intercept) so that communication is clear.
Students should have an opportunity to discuss answers to the questions on effect of parameters with at least a partner and perhaps a small group before the large group discussion.
Introduction of a symbolic method to determine axis of symmetry is optional at this point. Some general discussion of role of a and b may be sufficient at this time. (signs related to shift)
An introduction to the activity should include directions for the student to:
Make a "good" but not necessarily point-perfect sketch of the graphs.
To think about the relation between the parameters and the graph as they are working through the examples.
In some way, students should be introduced to vocabulary (parabola, symmetry, parameter, y-intercept) so that communication is clear.
Students should have an opportunity to discuss answers to the questions on effect of parameters with at least a partner and perhaps a small group before the large group discussion.
Introduction of a symbolic method to determine axis of symmetry is optional at this point. Some general discussion of role of a and b may be sufficient at this time. (signs related to shift)
Student Activity help
Three groups of quadratic and linear rules to explore: on Web page
Assessment help
A quiz matching rules and graphs is provided.
Completion of the activity, observation during discussion or student reports could also provide information on student learning.
Completion of the activity, observation during discussion or student reports could also provide information on student learning.
Enrichment / Alternative Activity help
Students might create function rules of their own and predict graph appearance.
Depending on the grade level, discussion of symbolic techniques for graph descriptors.
Discussion of vertex and x-intercepts.
Depending on the grade level, discussion of symbolic techniques for graph descriptors.
Discussion of vertex and x-intercepts.
Technology Requirements/Integration help
Students must have a graphing utility. Either a computer or
graphing calculator will be fine. A utility where the whole
rule is entered may be used or one may be available where
you only need to enter a, b, c.
Student printouts may be required if students have ability
to paste the graphs into a document.
graphing calculator will be fine. A utility where the whole
rule is entered may be used or one may be available where
you only need to enter a, b, c.
Student printouts may be required if students have ability
to paste the graphs into a document.