Question

Anne fires a toy rocket into the air from the top of a barn. The height of the rocket above the ground in feet after t seconds is given by
the function h(t) = -5t^2 + 20t -15. After completing the trajectory, Anne finds that the maximum height the toy rocket reached in the
air is represented by the expression -5(t-__)^2+5 Write the missing piece of the expression

Answer 1

The missing piece of the expression is 2

Maximum height of the rocket

From the question, the height of the rocket above the ground in feet after t seconds is given by the function h(t) = -5t^2 + 20t -15

At maximum height, the velocity of the function is zero. Hence;

dh/dt - -5(2)t + 20
dh/dt = -10t + 20

Write the expression in vertex form as shown:

h(t) = -5t^2 + 20t -15

h(t) = -5(t^2 - 4t +3)

h(t) = -5(t^2 - 4t + 2^2 + 3 - 2^2)

h(t) = -5((t+2)^2 +5
h(t) = -5((t+2)^2 + 11

Hence the missing piece of the expression is 2

Learn more on vertex form here: https://brainly.com/question/525947