Math Council 3/16/2018 – Quadratics 1) y = 5x2 + bx + c and this parabola intersects the x-axis at (10, 0) and (-3, 0). a. What are b and c? 2) Recall that v = dx/dt. a. If x = 3t + 7, v = ? b. If x = 4t2 + 5t + 3, v = ? c. If x = 5t3, v = ? 3) If you fire a rock up in the air and it has a trajectory of x = 100t – 10t2 a. At what time does the rock land back on the ground? b. At what time is the rock at its peak (when v = 0) c. What height did the rock reach? 4) You have bought fencing with a total length of L feet to surround a rectangular garden. What is the maximum area that you can make the garden? What are the length and width of the garden? 5) You have bought fencing with a total length of L feet to surround a rectangular garden, but this time you already have a pre-existing wall of length A that you can connect the fence to (giving you an extra A feet of protection). What is the maximum area that you can make the garden? 6) Your team is selling Bigelow Math Council T-shirts. You currently charge $20 per T-shirt and average 40 sales per week. Based on a recent study at MIT about T-shirt sales, you learn that for every fifty-cent increase in price, the average business can expect to lose 4 sales per week. Use this information to attempt to maximize your income. What should you charge, and how much more will you make per week than you do now?