quadratic function whose graph is a parabola containing the given points.

Question

An egg is dropped from the top of a 576-foot-high building. The ball is 432 feet above the ground after 3 seconds, and it reaches level ground in 6 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

Answer 1

576 feet tall when t=0

432 feet after t=3

0 feet after t=6

h(t) =-16t^2 +576

h(0) = 576

h(3) = -144+576 = 432

h(6) = -16(6^2) +576 = 0

general equation is h(t) =(a/2)t^2 +vot +ho

where vo = initial velocity = 0 feet per second

ho = initial height = 576 feet

a= -32 feet per second per second = aceleration due to gravity