3. A rocket is launched vertically from a platform that is 48 ft from the ground with an initial velocity of 32.

Question

(a)  Write a quadratic function  that shows the height, in feet, of the rocket t seconds after it was launched.

(b)  Determine the rocket’s maximum height and the amount of time it took to reach its maximum height, and the amount of time it was in the air. Be sure to show your work to receive credit.

(c)  Graph on the coordinate plane.

Answer 1

h(t) = -16t² + 32t + 48

take the derivative and set it equal to zero to find maximum height

h'(t) =-32t +32 = 0

t=32/32 = 1 second

plug 1 into the original equation for h(t)

h(1) = -16 +32 + 48 = 64 feet at maximum height, after one second

The graph is a parabola, with axis of symmetry at t=1, where h is a maximum. The parabola opens downward.

plot h on the y axis and t on the x axis.

The parabola intersects the y-axis at (0,48) and intersects the x-axis at (3,0) when it hits the ground in 3 seconds. It has a maximum at its vertex (1,64)