SOLUTION: A ball tossed into the air follows a parabolic trajectory. Its height after t seconds is given by a polynomial of degree two with leading coefficient -16. Using synthetic substit

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Question 383957: A ball tossed into the air follows a parabolic trajectory. Its height after t seconds is given by a polynomial of degree two with leading coefficient -16. Using synthetic substitution, Norman found that the polynomial evaluates to 0 for the values t = 0 and t = 4. What is the polynomial that describes the ball's height as a function of t?
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A ball tossed into the air follows a parabolic trajectory.
Its height after t seconds is given by a polynomial of degree two with leading coefficient -16.
Using synthetic substitution, Norman found that the polynomial evaluates to 0
for the values t = 0 and t = 4.
What is the polynomial that describes the ball's height as a function of t?
:
The problem describes the trajectory equation: height = f(t)
h = -16t^2 + vt
The ball strikes the ground when t = 4, so we have
-16(4^2) + 4v = 0
To complete the equation find v
-16(16) + 4v = 0
-256 + 4v = 0
4v = 256
v = 256%2F4
v = 64, the upward initial velocity
:
f(t) = -16t^2 + 64t, describes the height of the ball in t seconds