Luca is in a culvert below street level. He launches an object at an upward velocity of 40 feet per second. Use GeoGebra to graph the situation using the formula y=−16t2+40t−5

Question

𝑦
=
−
16
𝑡
2
+
40
𝑡
−
5
. How far above or below street level is Luca’s initial launching point?(1 point)
Responses

2.5 feet below
2.5 feet below

5 feet above
5 feet above

0 feet above or below
0 feet above or below

5 feet below

Answer 1

The equation provided, \( y = -16t^2 + 40t - 5 \), represents the height \( y \) (in feet) of the object over time \( t \) (in seconds). The term \( -5 \) indicates the initial height of the object when \( t = 0 \).

To find Luca's initial launching point, substitute \( t = 0 \) into the equation:

\[ y(0) = -16(0)^2 + 40(0) - 5 \] \[ y(0) = -5 \]

Thus, the initial height is \( -5 \) feet, indicating that Luca's launching point is 5 feet below street level.

Therefore, the correct response is: 5 feet below.