The height that a baseball reaches when it is thrown can be modeled by the function h(t) = -16 (t - 1.5)^2 + 36

Question

a. What happens to the ball between t = 0, and t = 1.5 seconds?

b. Describe the transformation of h from the parent function f(t) = t^2.

c. What is the maximum height of the baseball?

d. How long does it take to reach its maximum height?

e. Draw a graph of the baseball's path.a

Answer 1

height = 36 feet at time t=1.5 seconds

height = 36-16(2.25) =0 at time t=0

it goes up from the ground level to 36 feet high in the first 1 1/2 seconds

t^2

shift right 1.5

= (t-1.5)^2

stretch 16

=16(t-1.5)^2

reflect about the x axis

=-16(t-1.5)^2

shift up 36

= -16(t-1.5)^2 +36

max height = 36 feet

it takes 1 1/2 seconds reach max height

graph is a downward opening parabola

plot 3 points: vertex=max h = (1.5, 36)

axis of symmetry: x= 1.5

x,y intercept (0,0)

symmetric point (3,0) in 3 seconds it hits the ground

connect the 3 points with a smooth parabolic shaped curve