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?