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Here is a Picture of what it should look like

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Here is a Picture of what it should look like

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The π-rates: Ian Kirner, Julia Jankowski, Kate Ullem

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The π-rates: Ian Kirner, Julia Jankowski, Kate Ullem

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The Polycheerios: Isabelle Carlson, Heather Chen, Natalie Tsimhoni, & Clarise Zajac

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The Polycheerios: Isabelle Carlson, Heather Chen, Natalie Tsimhoni, & Clarise Zajac

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A model rocket is launched into the sky. The equation to model this situation is y=-x^2+40x-200. Find the maximum height in feet.

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The Quartics: Jonathan Margosian, Jacob Lepley, Ayla Rafiq and Maria Yankelevich.

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The Quartics: Jonathan Margosian, Jacob Lepley, Ayla Rafiq and Maria Yankelevich.

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The Big Al throws a stone from the 50-yard line on the football field straight up because he is mad about how the band is performing. The stone takes 12 seconds to hit the ground and just misses a flute player. What is the highest point the stone traveled to (in meters) and how long did it take (in seconds)? What would be the equation in vertex form?

To Solve:

You know that you start at ground level and at 0 seconds, so your first point would be (0,0). You also know that it takes 12 seconds for the stone to come down, so you know the point (12,0). These are your x-intercepts and with those, you can write the equation; y=-x(x-12). With the equation, you can find the AOS, which is x=6 and solve to find the vertex, which would be the highest point of the stone. So you put 6 in for x and solve for y.  When you solve you should find that y=36. So you would find out that the stone, in 6 seconds, traveled 36 meters up into the air.

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The  π-rates: Ian Kirner, Julia Jankowski, Kate Ullem

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The  π-rates: Ian Kirner, Julia Jankowski, Kate Ullem

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A dolphin is swimming in the ocean and starts low in the ocean then jumps out of the water once, then skims the ocean and jumps again but not as high the second time, then swims down to the bottom of the ocean again. If the graph looks like this: then what is the equation?

Answer Key:
To solve this you first need to find the degree and if the leading coefficient is negative or positive. The degree is even because the graph goes down down which also means that the leading coefficient is negative. Now we need to determine the x-ints. They are (3, 0), (0, 0) and (2, 0) by looking at the graph. Right now the equation is y= -x (x + 3)(x - 2) but we are not done yet. Now, all we need to determine are the exponents. The (0, 0) is a double because it bounces off the x-axis. And the other ones are singles because it goes through the x-axis without a curve. Our final equation is y= -x^2 (x + 3)(x - 2).

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Aidan and Wei-jie Team Name: Cubed roots

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Aidan and Wei-jie Team Name: Cubed roots

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A contractor wants to put in a window 3x +10 by 2x+6 feet. What is the area of the window?

6x^2 +38x+60

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The Algebros: Megan DeFrancesco, Aerin Wash, & Anja Weller

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The Algebros: Megan DeFrancesco, Aerin Wash, & Anja Weller

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You are manager at a theme park. Recently, your company decided to create a new roller coaster that dips underground. But, while writing the blueprints, your team realised they never planned where they need to dig holes for the roller coaster to enter. The roller coaster starts at the ground, and the equation that models the roller coaster’s path of travel is y=x^2(x^2- 10x+24)(x-9)^3, where x represents the number of kilometers from the starting point of the roller coaster, and y represents the height of the roller coaster in kilometers . Find where the holes need to be dug, and where the roller coaster ends, using the image below.

1. Completely factor the equation by foiling to get y=x^2(x-4)(x-6)(x-9)^3

2. Find all of the x intercepts or points where the roller coaster touches the ground (x-axis): (0,0)D, (4,0), (6,0),  (9,0)T

3. We know the coaster starts at 0 and ends at the highest number of kilometers away, so the holes must be dug at 4 kilometers and 6 kilometers, and the roller coaster will end at 9 kilometers.

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The Algegals: Caitlin Drouse, Shannon Carraway, Emma Abramyczyk, and Savitri Anantharaman

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The Algegals: Caitlin Drouse, Shannon Carraway, Emma Abramyczyk, and Savitri Anantharaman

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A basketball was shot from 5 feet off the ground with a velocity of 20 f/s. The height of the ball is modeled by the equation h=-16t2+24t+6, with t being the time in seconds and h being the height. Based on this equation, what is the maximum height of the ball and how long does it take to reach it?