Question

a rocket is fired upward from ground level with an initial velocity of 534.1 m/sec. the height of the rocket ( s(t) ) in meters is a function of the time ( t ) in s after launch.

( s(t)=-4.9 t^{2}+534.1 t )

part 1 of 4

(a) what characteristics of ( s ) indicate that it is a quadratic function?

the function ( s ) is quadratic because it is in the form ( s(t)=a t^{2}+b t + c ), where ( a
eq 0 ).

part: ( 1 / 4 )

part 2 of 4

(b) find the ( t )-intercepts of the function.

the ( t )-intercepts are ( (quad,quad) ) and ( (quad,quad) ).

Explanation:

Step1: Set \(s(t) = 0\)

$$ -4.9t^{2}+534.1t = 0 $$

Step2: Factor out \(t\)

$$ t(-4.9t + 534.1)=0 $$

Step3: Solve for \(t\)

Using the zero - product property \(ab = 0\Rightarrow a=0\) or \(b = 0\).
If \(t=0\), then one solution is \(t = 0\).
If \(-4.9t+534.1 = 0\), then \(-4.9t=-534.1\), and \(t=\frac{-534.1}{-4.9}=109\).

Answer:

The \(t\) - intercepts are \((0,0)\) and \((109,0)\)