Algebra 1 PARCC: Where’s the parabola?

The following multi-part 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 2016 test in algebra 1 (#7), here:

The parabola   f(x) = (x-2)^2 + 1   is graphed in the xy-coordinate plane.

Part A

What is true about the vertex of the parabola?

  1. It is 2 units to the left of the origin and 1 unit down from the origin.
  2. It is 2 units to the right of the origin and 1 unit up from the origin.
  3. It is 2 units up from the origin and 1 unit to the right of the origin.
  4. It is 2 units down from the origin and 1 unit to the left of the origin.

Part B

How does the graph of the function f(x+3) compare to the graph of f(x) ?

  1. f(x+3) has a vertical shift 3 units up from f(x) .
  2. f(x+3) has a vertical shift 3 units down from f(x) .
  3. f(x+3) has a horizontal shift 3 units to the right of f(x) .
  4. f(x+3) has a horizontal shift 3 units to the left of f(x) .
Answer and references
Example of a solution strategy (there are others)

Online resources for further study

Analysis of this question and online accessibility

The question measures knowledge of part of the Common Core standard it purports to measure and tests students’ ability shift, translate, and stretch the graph of a parabola on the coordinate plane.

The question can be tested online and should yield results that are as valid and reliable as those obtained on paper. In addition, no special accommodation challenges can be identified with this question, so the question is considered fair.

However, the multiple-choice format adds unnecessarily to the reading load for the question, given that other presentation options are available in an online format. The question is equivalent online in that the paper-and-pencil version of this item will be identical to the online version, but since more than 90 percent of students take the test online, at least in Maryland, a better presentation option would have been more appropriate here.

Furthermore, multiple-choice options like this, where all but one or two words are identical, can confuse students who have a reading disability. Especially in Part B where the order of the vertical shift and horizontal shift is different in options C and D from what it was in options A and B (this is done to conform to a convention in multiple-choice options that present them in two pairs of two options), the re-reading of nearly similar answer options can be confusing. It’s not terrible here, though, since the answer options are just one line each, but if they include more than one sentence, other options for presentation should be explored.

About the Author

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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