In this assessment, you will take on the role of a roller coaster engineer. You are...

   

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In this assessment, you will take on the role of a roller coaster engineer. You are to create a roller coaster, its equation, and it associated graph. You must include all requirements along with a sketch/graph and equation of your roller coaster. The roller coaster can go above and/or below 'ground-level'. Assume the x-axis is 0 m above ground level and the y-axis is 0 m from the beginning. Your roller coaster must be modelled by a polynomial function that: Is degree 3 or 4 Has at least one double or triple root Has at least one positive and one negative x-intercept In designing your roller coaster, you must answer the following questions: 1) What do you want the starting and ending behaviours of your roller coaster to look like and why? How can you ensure your function will accomplish these end behaviours? (3 marks) 2) Where do you want the roller coaster to be at ground-level and why? How can you ensure your function and its equation will accomplish this? (3 marks) 3) At these ground-level points, do you want the roller coaster to cross ground-level or just to touch it and why? How can you ensure your function will accomplish this? (3 marks) 4) Create an equation that can model your roller coaster. Write it in factored form. (5 marks) 5) Sketch your graph without using technology based on the end behaviours, leading coefficient, and x-intercepts and their orders. (5 marks) 6) Using technology question 4. (2 marks) graph the function you created in 7) Reflect on your graph in 6), is there anything you would change about your function? Explain why, or why not. (3 marks) In this assessment, you will take on the role of a roller coaster engineer. You are to create a roller coaster, its equation, and it associated graph. You must include all requirements along with a sketch/graph and equation of your roller coaster. The roller coaster can go above and/or below 'ground-level'. Assume the x-axis is 0 m above ground level and the y-axis is 0 m from the beginning. Your roller coaster must be modelled by a polynomial function that: Is degree 3 or 4 Has at least one double or triple root Has at least one positive and one negative x-intercept In designing your roller coaster, you must answer the following questions: 1) What do you want the starting and ending behaviours of your roller coaster to look like and why? How can you ensure your function will accomplish these end behaviours? (3 marks) 2) Where do you want the roller coaster to be at ground-level and why? How can you ensure your function and its equation will accomplish this? (3 marks) 3) At these ground-level points, do you want the roller coaster to cross ground-level or just to touch it and why? How can you ensure your function will accomplish this? (3 marks) 4) Create an equation that can model your roller coaster. Write it in factored form. (5 marks) 5) Sketch your graph without using technology based on the end behaviours, leading coefficient, and x-intercepts and their orders. (5 marks) 6) Using technology question 4. (2 marks) graph the function you created in 7) Reflect on your graph in 6), is there anything you would change about your function? Explain why, or why not. (3 marks)