While on the Power Tower ride at Valleyfair, you throw a
marble upwards from the very top of the ride with an initial
velocity of 50 feet per second. (The ride was supposed to be 25
feet taller, but the Federal Aviation Administration said, “no!”)
The height of the marble can be modeled with the equation
given by ℎ(t) = −16t^2 + 50t+ 250, where ℎ is in feet and t is
in seconds.
a. Graph the parabola on your calculator. Adjust the window
so you can see the vertex and the x- and y-intercepts.
b. What is the maximum height of the marble? How many
seconds did it take to reach this height?
Max height: __________ Time: __________
c. How high above the ground is the marble at t = 3 seconds?
Height: ____________
d. Accurate to three decimal places, when does the marble hit the ground?
Time: _____________
for at^2+bt+c, the vertex is at t = -b/2a
Now you can answer (b) and (c)
(d) solve −16t^2 + 50t+ 250 = 0 in the usual way