# Algebra HELP – Word Problem#1 – Roller Coaster Crew

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Roller Coaster Crew

Ray and Kelsey possess summer internships at an engineering stable. As separate of their internship, they get to befriend in the paintning of a stigma new roller coaster. For this assignment, you aid Ray and Kelsey as they paraphernalia the math after some elementary incurvations in the coaster's trace.

Part A

The foremost separate of Ray and Kelsey's roller coaster is a tortuous paint that can be represented by a polynomial business.

1. Ray and Kelsey are afloat to graph a third-degree polynomial business that represents the foremost paint in the coaster paint. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the business can possess as multifarious as 3 zeros simply. Is there a way for the twain of them to be amend? Explain your apology.
2. Kelsey has a schedule of likely businesss. Pick one of the g(x) businesss beneath and then depict to Kelsey the key features of g(x), including the end deportment, y-intercept, and zeros.
• g(x) = x3 − x2 − 4x + 4
• g(x) = x3 + 2x2 − 9x − 18
• g(x) = x3 − 3x2 − 4x + 12
• g(x) = x3 + 2x2 − 25x − 50
• g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial business you chosen from Question 2.

Part B

The relieve separate of the new coaster is a parabola.

1. Ray needs aid creating the relieve separate of the coaster. Create a matchless parabola in the paint f(x) = ax2 + bx + c. Depict the command of the parabola and particularize the y-intercept and zeros.
2. The prophylactic director notes that Ray so needs to paint for a upright ladder through the benevolence of the coaster's parabolic model for advance to the coaster to execute prophylactic repairs. Find the vertex and the equation for the axis of intercoincidence of the parabola, showing your effect, so Ray can grasp it in his coaster paint.
3. Create a graph of the polynomial business you created in Question 4.

Part C

1. Now that the incurvation pieces are particularized, use those pieces as individualitys of a adequate coaster. By laborer or by using a contrivance program, paint a artfulness of Ray and Kelsey's coaster that grasps the model of the g(x) and f(x) businesss that you chose in the Parts A and B. You do not possess to grasp the coordinate painte. You may deal the businesss in any regulate you cull, but designate each individuality of the graph after a while the identical business for your schoolmistress to estimate.

Part D

1. Create an ad engagement to excite Ray and Kelsey's roller coaster. It can be a 15-relieve notice for television or radio, an interestimate for a recipient or tidings reverberation, or a lyric, anthem, or slideshow introduction for a community. These are fair examples; you are not scant to how you provide your notice, so be imaginative. Make enduring to grasp a script of what each of you conciliate say if you are preparing an interestimate or a reverberation. The end of this ad is to get everyone dazed encircling the roller coaster.

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