May’s class is testing their egg protection contraptions by dropping them off the roof of their school. Use GeoGebra to graph the situation using the formula y=−16t2+40

Question

𝑦
=
−
16
𝑡
2
+
40
. Which of the following correctly interprets the height of the school’s roof?(1 point)
Responses

20 feet
20 feet

41 feet
41 feet

40 feet
40 feet

15 feet

Answer 1

To interpret the height of the school's roof in the context of the equation \( y = -16t^2 + 40 \), we need to analyze the equation.

In this equation:

• \( y \) represents the height of the egg protection contraption (in feet).
• \( t \) represents time (in seconds).

The term \( -16t^2 \) indicates that the height of the contraption decreases over time due to the effect of gravity, which accelerates the drop. The constant term, 40, represents the initial height from which the egg protection contraption is dropped at \( t = 0 \).

Therefore, when \( t = 0 \): \[ y = -16(0^2) + 40 = 40 \]

This means that the height of the school's roof is 40 feet.

So, the correct interpretation of the height of the school’s roof is 40 feet.