Question

question 18 of 20 (1 point) | question attempt: 1 of 3

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

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 2 of 4

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

the t-intercepts are $(0,0)$ and $(109,0)$.

part: 2 / 4

part 3 of 4

(c) what do the t-intercepts mean in the context of this problem?

the t-intercepts indicate that the rocket is at ground level (height $s(t)=\square$) at $\square$ sec and $\square$ sec.

Explanation:

Step1: Find the \(t\)-intercepts

Set \(s(t)=0\), so \(-4.9t^{2}+534.1t = 0\).
Factor out \(t\): \(t(-4.9t + 534.1)=0\).

Step2: Solve for \(t\)

Using the zero - product property:
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 \((109,0)\).