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Regents Recap — June 2014: These Are Not Parabolas

Here is another installment in my series reviewing the NY State Regents exams in mathematics.

I have written extensively about the unfaithful graphs presented on Regents exams:  non-trigonometric trig functions, non-exponential exponential functions, “functions” that intersect their vertical asymptotes multiple times.  I really don’t understand what is so hard about putting accurate graphs on tests.

Here is this year’s example.  These are some of the ugliest “parabolas” I have ever seen.  I can’t look at these without being mathematically offended.

regents 2014 -- ugly parabolas

Not one of these graphs are parabolas.  Take a closer look at (3), by far the ugliest purported parabola.  Look at how unparabolic this is.  It lacks symmetry, and appears to turn into a line at one point!

the ugliest parabola

If this were truly a parabola, we would be able to fit an isosceles triangle inside with vertex on vertex.

the ugliest parabola plus triangle

Not even close!

It’s a fun exercise to show that the others can’t possibly be parabolas either, which I will leave as to the reader.

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