Question

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−5𝑦=−16𝑡2+40𝑡−5. How far above or below street level is Luca’s initial launching point?(1 point)Responses5 feet below 5 feet below 5 feet above5 feet above2.5 feet below2.5 feet below0 feet above or below

Answer 1

To determine how far above or below street level Luca's initial launching point is, we will analyze the equation given:

\[
y = -16t^2 + 40t - 5
\]

In this equation:
- \(y\) represents the height of the object in feet,
- \(t\) is the time in seconds,
- The term \(-5\) represents the initial height (launching point) of the object.

Since the equation shows that when \(t = 0\) (the moment of launch), we can substitute \(t = 0\) into the equation to find the initial height:

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

This means Luca's initial launching point is 5 feet below street level.

Thus, the answer is **5 feet below**.