Question

Terry throws a ball straight up. The initial height of the ball is 3 feet and has an initial velocity of 32 feet per second. The function is modeled by:

h(t) = -16t2 + 32t + 3
a) What are the coordinates of the vertex of the parabola?
b) What do the coordinates of the vertex of the parabola mean in the context of this problem?
-How high off the ground will the ball be after 2 seconds? Show your work.
-What is the height of the ball at 0.5 seconds and 1.5 seconds after being thrown? Why is the height the same at .5 seconds and 1.5 seconds
a) How long is the ball in flight?

Answer 1

a) How long is the ball in flight? Round answer to nearest hundredth.

b) Which formula, process, etc. did you use to solve this problem?

Answer 2

\(h(t) = -16t2 + 32t + 3\)
\(y=at^2+bt+c\) first coordinate of the vertex is always \(-\frac{b}{2a}\)
second coordinate is what you get when you replace \(t\) by that number

Answer 3

the ball is in flight for as long as it takes to hit the ground, set
\[-16t^2+32t+3=0\] and solve for \(t\)

Answer 4

H(t) = -16(t^2 - 2t + ___) + 3
= -16( t^2 -2 +1) +16 +3
= -16(t+1)^2 + 18

the co ordinates of a vertex is (-h,k)
from the formula a(x-h)^n + k

Answer 5

b) Which formula, process, etc. did you use to solve this problem?

i used the process of asking on open study