Question

Please Help!!!!

A ball was thrown upward into the air. The height in feet of the ball, above the ground, t seconds after being thrown can be determined by the expression -16t² + 40t + 3. What is the meaning of the 3 in the expression?
A.) the ball took three seconds to reach its maximum height
B.) the ball took three seconds to reach the ground
C.) the ball was thrown from a height of three feet
​D.) the ball reached a maximum height of three feet

Answer 1

The ball was thrown from a height of
`3\; {\rm ft}`.

Explanation:

The expression for the height of this ball,
`h(t) = -16\, t^(2) + 40\, t + 3`, represents a parabola (with respect to time
`t`.)

In this expression, "
`3`" represents the
`y`-intercept of the parabola- the output of the parabola when the input is
`t = 0`. The reason is that when
`t = 0\!`, terms of this parabola that include
`t` (
`(-16\, t^(2))` and
`40\, t`) would evaluate to
`0`:

`\begin{aligned}h(0) &= -16* 0^(2) + 40* 0 + 3 = 3\end{aligned}`.

In the case of this ball, the term "
`3`" means that height of this ball is
`3\; {\rm ft}` when
`t = 0` (right when the ball was thrown.) Thus, the ball was thrown from a height of
`3\; {\rm ft}`.