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Peer Review

Effect of Coefficient of x^2 on Parabola Vertex (a>0)

by James Rutledge


Overall Numeric Rating:

5 stars
Content Quality: 5 stars
Effectiveness: 5 stars
Ease of Use: 5 stars
Reviewed: Apr 09, 2011 by Mathematics
Overview: This site is part of a collection of ready-made interactive classroom activities in mathematics hosted by the MERLOT Math Pedagogic Collection and the Science Education Resource Center (SERC) Pedagogic Service Portal for educators. The home page at explains that “making lectures interactive draws students into the lecture by engaging them in working with the material. In an interactive lecture, the lecture is interspersed with short individual, pair, or small-group activities. These activities also provide feedback to the instructor on student understanding.” A list of the various math examples and interaction types is available at Reviews of other specific pages can also be found at MERLOT. In general the activities include some or all of a five minute “ConcepTest” – where the individual student answers a question and the instructor polls the class, a ten minute Question of the Day – where the student works with a neighbor and records their conclusions in writing, and a fifteen minute Write-Pair-Share activity where students collaborate to refine and expand on the original discussion. The activity also includes a link to an interactive Java applet where the instructor can demonstrate the concepts that the students have been exploring. This particular page (#48744) is one of six that examine the behavior of the graph of a parabola as the values of the coefficients are changed. Specifically it encourages student exploration of the effect of changing the value of a positive coefficient of x^2 on the vertex of a parabola where a>0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c.
Type of Material: tutorial, drill & practice
Recommended Uses: The main use of the material is as a part of in-class activity.
Technical Requirements: Ability to display Word rtf documents in browser. Java enabled browser with Flash Player for instructor demonstration portion.
Identify Major Learning Goals: The learning goal of this material is to develop students’ understanding of the effects of coefficients in quadratic functions through exploration and discussion with fellow students.
Target Student Population: Students taking college algebra
Prerequisite Knowledge or Skills: Some knowledge of basic algebra.

Evaluation and Observation

Content Quality

Rating: 5 stars
Strengths: This site contains a ready-to-use in-class activity module that consists of the ConcepTest, Question of the Day, Write-pair-share exercise, and conclusion involving the use of a demonstration applet. Each part is performed by students in succession and is meant to develop student’s understanding of the algebraic and mathematical analysis involving the expanded form of the formula for the vertex of parabola by clearly explaining how the coefficient of x^2 affects each of the x- and y-coordinates of the vertex. There are five other related modules that explore the graph of a parabola.
Concerns: Notice that while there are six parabola activities, they all use the same interactive demonstration applet and parameters must be adjusted to match the case under investigation.

Potential Effectiveness as a Teaching Tool

Rating: 5 stars
Strengths: An instructor can use this activity “out of the box”. It can be carried out in either a small College Algebra class or a large lecture setting anytime during or after the topic of graphing quadratic functions has been covered.
Concerns: None.

Ease of Use for Both Students and Faculty

Rating: 5 stars
Strengths: The detailed instruction and clear structure of this module makes it very easy to use. Since it is part of a series of activities in similar format the instructor can build familiarity with the nature of such activities throughout the course.
Concerns: The display of the Word rtf files in Windows Explorere seemed surprisingly temperamental.