Problema Solution
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function f(t)=-16t^2+16t+480, where t is the time in seconds and h is the height in feet.
a.) How long did it take for jason to reach his maximum height?
b.) What was the highest point that jason reached?
c.)Jason hit the water after how may seconds?
Answer provided by our tutors
Note: the vertex form of a parabola,
where(h,k) is the vertex
h(t)= -16t² + 16t + 480 Believe there should be a minus squared term
h(t)= -16t^2 + 16t + 480 completeing the square to find the vertex
h(t)= -16(t^2 - t) + 480
h(t)= -16[(t - 1/2)^2 - 1/4] + 480
h(t)= -16(t - 1/2)^2 + 4 + 480
h(t)= -16(t + 1/2)^2 + 484 vertex is Pt(1/2,484) or ordered pair (t,h(t))
a. How long did it take for Jason to reach his maximum height? 1/2 sec
b. What was the highest point that Jason reached? 484ft
c. Jason hit the water after how many seconds?
h(t)= 0 = -16t² + 16t + 480
t = 160/32 = -5 extraneous solution
t = 192/32 = 6 sec