Quadratic Function Modeling Rocket
View group questions.
To print this group, add it to a test.
A small model rocket is launched straight up into the air. After rising to its highest point, its parachute fails to open and the rocket falls straight back to the ground. Let [math]h(t) = -4.9t^2 + 30t[/math] represent the height of the rocket in meters, dependent on the time, [math]t[/math], in seconds. The function is only valid for times [math]t[/math] such that [math]t[/math] is greater or equal to the start time and less than or equal to when it hits the ground.
A.
Complete the square so that the function [math]h(t)[/math] is in vertex form. Which of the following is correct? Round computed coefficients and terms to one decimal place, if necessary.
- [math]h(t) = -4.9(t - 3.1)^2 - 9.4[/math]
- [math]h(t) = -4.9(t - 3.1)^2 + 45.9[/math]
- [math]h(t) = (-4.9t + 15)^2 - 225[/math]
- [math]h(t) = -4.9(t + 3.1)^2 + 9.4[/math]
B.
What facts about the rocket can be seen directly from the vertex form of the function? Choose all that apply.
- The time when the rocket reached its maximum height.
- The total duration of the rocket's flight.
- The initial velocity of the rocket.
- The rocket's maximum height.
C.
Which of the following is the correct fully factored form of the function [math]h(t) ?[/math]
- [math]h(t) = (2.2t - 5.5)(2.2 + 5.5)[/math]
- [math]h(t) = 4.9(t^2 + 6.1t)[/math]
- [math]h(t) = -4.9t (t - 6.1)[/math]
- [math]h(t) = (-4.9t - 3)(t + 10)[/math]
D.
What information about the rocket can be directly seen from the factored form of [math]h(t) ?[/math] Choose all that apply.
- The initial height height.
- The total duration of the flight.
- The velocity when the rocket reaches its maximum height.
- How far the rocket traveled.
