The following multiple-choice question, explained here in hopes of helping algebra students in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2015 test in algebra 1, here:
Which is the graph of the function ?
Resources for further study
Purple Math, developed by Elizabeth Stapel, a math teacher from the St Louis area, has a four-part series on graphing quadratic functions on a coordinate plane. She explains that, while you may start your graph by plotting points at integer x values, you have to finish the graph by drawing a smooth curve in between the points so that all points in the function’s domain, including those between the integers, are represented. The series starts here.
The Khan Academy, developed by Sal Khan, an engineer who has created a library of thousands of video lessons, has a few that demonstrate how to graph quadratic function (parabolas) on the coordinate plane. The series starts here, with “Intro to Parabolas.”
Chapter 5, Section 5-2 of Paul A Foerster’s book Algebra and Trigonometry deals with quadratic function graphs. He He advises, “the vertex is the most important point on the graph of a quadratic function. If you know where the vertex is, you can sketch a reasonably good parabola with very little other information.”
Complete reference: Foerster, Paul A. Algebra and Trigonometry: Functions and Applications, revised edition. Addison-Wesley, 1980, 1984. The book is used in several algebra classes taught in middle and high schools in both Illinois and Maryland.
Analysis of this question and online accessibility
The question measures knowledge of the Common Core standard it purports to measure and tests students’ ability to recognize that the graph of a function in the coordinate plane includes all points in the domain, even those that fall in between the grid lines on the graph. It is considered to have a low cognitive demand.
The question can be tested online and should yield results that are as valid and reliable as those obtained on paper. The multiple-choice format may promote guessing, which casts doubt on the validity of the question.
No special accommodation challenges can be identified with this question, so the question is considered fair.
How would you define a function that has a domain that looks like (A), (B), or (C)? Can you identify a real-world situation that might have such a graph?
Purpose of this series of posts
Voxitatis is developing blog posts that address every algebra 1 question released to the public by the Partnership for Assessment of Readiness for College and Careers, or PARCC, in order to help students prepare to take the test this spring.
Our total release will run from February 27 through March 15, with one or two questions discussed per day. Then we’ll move to geometry at the end of March, algebra 2 during the first half of April, and eighth grade during the last half of April.