Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 152047: A circus performer is juggling clubs while standing on stilts. He releases a club from a point 8ft above the ground with the initial vertical velocity of 10 ft per second.
The vertical motion mode is h = -16t2(It's t to the second power) + vt + s where he is the height of an object in feet, t is the time seconds, v is the initial vertical velocity in feet per second, and s is the initial height in feet.
a) Write an equation in function notation that models the height (in feet) of the club as a function of time (in seconds).
b) Make a table of the time in the air and the heights of the club from 0.1 seconds to 1.5 seconds.
c) Graph the function and label the vertex.
d) How long after the club is released does the club reach its maximum height? What was the maximum height?
e) How long after the club is released will it return to the ground? How do you know this?

Thanks so much for your help!!!!
: A circus performer is juggling clubs while standing on stilts. He releases a club from a point 8ft above the ground with the initial vertical velocity of 10 ft per second.
The vertical motion mode is h = -16t2(It's t to the second power) + vt + s where he is the height of an object in feet, t is the time seconds, v is the initial vertical velocity in feet per second, and s is the initial height in feet.
a) Write an equation in function notation that models the height (in feet) of the club as a function of time (in seconds).
b) Make a table of the time in the air and the heights of the club from 0.1 seconds to 1.5 seconds.
c) Graph the function and label the vertex.
d) How long after the club is released does the club reach its maximum height? What was the maximum height?
e) How long after the club is released will it return to the ground? How do you know this?

Thanks so much for your help!!!!

Answer by vleith(1156) About Me  (Show Source):
You can put this solution on YOUR website!
You are given the equation
h = -16t^2 + v[0]t + s[0]
You are told the initial velocity is 10 feet/sec so v[0] = 10
You are told the initial position is 8 feet above the grouns. so s[0] = 10
Substitute that info into the equation to get
h = -16t^2 + 10t + 8
Plug in values for t from 0.1 through 1.5 and solve for h. You'll need to grind that out by hand., Just pick a few values for t and solve for h using the eqaution we just made.
graph the equation
graph(400,400, -1,3, -1, 11, -16x^2 +10x +8)
height is the y axis, time is the x axis.

To find the max height, look at the plot. Mark that point and then drop down to find the time and across to find the height


To find when it hits the round, set h = 0 and solve for t. Or look at the plot and find the time when the graph touches the x axis