Name ______________________________ Date ______________________________ Design a Roller Coaster Portfolio ALGEBRA 2 A: FUNCTIONS, EQUATIONS, AND GRAPHS Introduction: Have you ever ridden or seen a roller coaster in action? Did you know that the algebra that you have learned in this unit is related to the math that engineers use to design roller coasters? Engineers want roller coasters to be fun and scary, but also safe. Directions: For this portfolio, you will use your knowledge of functions to design a roller coaster. You will draw a short roller coaster on graph paper, plot ordered pairs on its path, and determine the slope, or rate of change, along the ride. Roller Coaster Design Instructions Submit responses to the following items, and be sure to show all of your work. 1. Draw the side view of your roller coaster on graph paper. For the sake of simplicity, assume that your roller coaster track never turns left or right. o In order to gain speed, the roller coaster should have an initial climb, at least two hills, and one loop. 2. Label the x- and y-axes. The value of x measures the horizontal distance from the roller coaster cart to the starting point, and the value of y represents the height of the roller coaster cart. (To make things easier it may be helpful to have the graph all in the first quadrant of the x-y plane, so all positive x and y-values) 3. Plot ordered pairs on the initial climb and determine the slope. (Try to make your paths straight rather than curved to make it easier to find slopes) 4. What is the equation of the line that represents your initial climb? (You may want to use point slope form y y 1 = m(xx 1) to help here) 5. What is the domain and range of your roller coaster? 6. Plot ordered pairs at the top and the end of each hill. Find the rate of change to determine which hill is steeper? How do you know that hill is steeper? (Your graph should have at least 2 hills so there should be at least 2 hills to consider for steepest but steepest could be either going up or coming down) 7. Is your roller coaster a function? Why or why not? (Use either the definition of a function or a test for functions using the graphs to help with this one.) Gr ap h of Ro lle r Co ast er Portfolio Self-Check List To be sure you are ready to turn in this portfolio please review the following check list.  My roller coaster starts off climbing upward  My roller coaster graph has at least 2 hills (including going up and down each) and a loop  I have shown my steps and/or explained reasoning for all of my answers for #3-7 *You do not need to turn in this check list, it is just for you to check with yourself