(1) the Roller Coaster Must Follow a Straight Path with No Loops

Name:______Period:______Date:______

Algebra 2 Unit 1 Puzzling Polynomial Performance Task 3

Roller Coaster Conundrum

Your engineering team has been asked to submit a proposal to an amusement park to design a new straight wooden roller coaster. The amusement park has requested that your design meet the following specifications:

(1) The roller coaster must follow a straight path with no loops.

(2) The roller coaster must start at ground level.

(3) At some point during the ride, the roller coaster must reach a height of at least 200 feet. This is important because the park wishes to capture the title as the park with the tallest wooden roller coaster. Currently Germany has a wooden roller coaster with a height of 197 feet.

(4) The park wants to advertise it as an ABOVE and BELOW ground level roller coaster. As a result, the roller coaster must go BELOW ground level at least ONCE.

(5) The park wants there to be at least one point on the roller coaster where the riders reach ground level, but then “bounce” back above/below ground level.

(6) The roller coaster must reach ground level at least THREE times throughout the course of the ride.

(7) The roller coaster must end at ground level.

It is the job of your engineering team to design the roller coaster that will satisfy your client’s requests. Your proposal must include a paragraph describing the roller coaster that your team has designed. You should also include a detailed sketch of your roller coaster. Your paragraph and sketch should include the following information:

(1) The polynomial equation (in standard form) that your roller coaster will follow.

(2) The factored form of your roller coaster.

(3) The starting height of your roller coaster.

(4) A written description of the path of the roller coaster including when the roller coaster is above and below ground level.

* Include the number of times the roller coaster will “bounce” on ground level.

* Include number of times the roller coaster reaches ground level.

(5) The distance the roller coaster has traveled when it ends at ground level.

(6) On your diagram, outline the graph in blue where the roller coaster is above ground level and

outline the graph in red where the roller coaster is below ground level.

*Remember, a roller coaster contract would mean a lot to your engineering team. Make sure you present a well-written, neat, and persuasive proposal as to why the amusement park should select your design over that of your competitors’ designs.

ADVANCED
(90-100%) / PROFICIENT
80%+ / PROGRESSING
70%+ / BEGINNING
50%+
☐Includes at least TWO below ground level portions.
☐Label 5 additional (non-zero) points on your graph.
☐State the domain of your polynomial equation.
☐State the range of your polynomial equation. / ☐Polynomial is written in standard form.
☐Polynomial is written in factored form.
☐Graph is sketched.
☐Graph is outlined in red and blue.
☐Graph is labeled with key points (starting point, ending point, points at ground level)
☐Paragraph is well written and explains the path of the roller coaster in words.
☐Rollercoaster meets the requirements listed in #1-7 above. / ☐Meets 4-5 of the “Proficient” requirements / ☐Meets fewer than 4 of the “Proficient” Requirements