Question

the height, h (in feet) of a model rocket launched from the roof of a building at t seconds is given by h = s(t)= - 16(t + 2)(t - 6). tells us if the graph opens up or down. it is 1/2 the acceleration of the object due to gravity. what does b represent? a. b is the maximum height b. b is the initial height of the object c. b is the initial velocity and the slope of the tangent line to the function at t = 0 d. b is the velocity when the height is maximum f. what does the value of c in the formula s(t)=at²+bt + c tell us about the object? a. c is the maximum height b. c is the initial height of the object c. c is the velocity when the height is maximum d. c is the initial velocity and the slope of the tangent line to the function at t = 0

Explanation:

For the position - time function $s(t)=at^{2}+bt + c$, the derivative $s^\prime(t)=2at + b$. At $t = 0$, $s^\prime(0)=b$, which is the initial velocity and the slope of the tangent line to the function at $t = 0$. Also, when $t = 0$, $s(0)=c$, which represents the initial height of the object.

Answer:

C. b is the initial velocity and the slope of the tangent line to the function at t = 0
B. c is the initial height of the object