June 2017: Common Core Algebra Regents, Part 3

The following are the questions and answers (and commentary) for part of the New York State Algebra Regents exam. If you have any questions or comments (or corrections), please add them in the Comments section.

My apologies for typos, particularly if they are in the questions, because then the answers are subject to change.

The answers to Part II can be found here.

June 2017, Algebra I (Common Core), Part III

33. The function r(x) is defined by the expression x² + 3x - 18. Use factoring to determine the zeroes of r(x).
Explain what the zeroes represent on the graph of r(x).

x² + 3x - 18 = 0
(x + 6)(x - 3) = 0
x + 6 = 0 or x - 3 = 0
x = -6 or x = 3 are the zeroes of the function

The zeroes of the function means that the graph will cross the x-axis at -6 and 3.

34. The graph below models Craig's trip to visit his friend in another state. In the course of his travels, he encountered both highway ad city driving.
Based on the graph, (image omitted) during which interval did Craig most likely drive in the city? Explain your reasoning.
Explain what might have happened in the interval between B and C.
Determine Craig's average speed, to the nearest tenth of a mile per hour, for his entire trip.

I would NOT want to grade this question. It assumes too much on the part of the students -- in particular, that you will travel more miles on the highway at a faster rate than in the city.

Second, you have to realize that the flat line between B and C means that the car is not moving at all (which is reasonable for the exam) but supposing why the car isn't moving. Did it stop on purpose? Is it stuck in traffic? Do cars get stuck in the city more than on the highway?

The answer that they are (probably) looking for is between points D and E, hours 5 and 7 when the rate of miles per hour has decreased, but the car is still moving. You wouldn't go as fast during city driving.

The 1.5 hours that the car was stopped was likely a stop in the trip and not driving at all.
Could be a rest stop. Could be a mall. Could be lunch. Could be a major traffic jam with a tree on the highway or a truck fire or a seven-car pile-up. I hope students get creative on this one!

Hint: to get the nearest tenth of a mile per hour, divide the total number of miles by the total number of hours: 230 miles / 7 hours = 32.8571428571, or 32.9 to the nearest tenth.

35. Given
g(x) = 2x² + 3x + 10
k(x) = 2x + 16
Solve the equation g(x) = 2k(x) algebraically for x, to the nearest tenth.
Explain why you chose the method you used to solve this quadratic equation.

g(x) = 2 k(x)
2x² + 3x + 10 = 2(2x + 16)
2x² + 3x + 10 = 4x + 32
2x² - x - 22 = 0

The Quadratic Formula is used in the image below:

Update: I cut the bottom from the image. Looks like I made a parenthesis error of some sort on the calculator and didn't catch it.

Calculate those fractions to the nearest tenth, and you get
x = 3.576... and x = -3.076, which round to x = 3.6 and x = -3.1

End of Part III


Answers to Part IV are here.

How did you do?
Comments, questions, corrections and concerns are all welcome.
Typos happen.