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May’s class is testing their egg protection contraptions by dropping them off the roof of their school. Use GeoGebra to graph t...Question
May’s class is testing their egg protection contraptions by dropping them off the roof of their school. Graph the situation using the formula y=−16t2+40 . Which of the following correctly interprets the height of the school’s roof?
Answers
GPT-4o mini
The formula \( y = -16t^2 + 40 \) represents the height \( y \) (in feet) of an egg protection contraption as a function of time \( t \) (in seconds) after it is dropped from the roof.
To interpret this situation:
1. **Initial Height**: When \( t = 0 \), the height \( y \) is:
\[
y = -16(0)^2 + 40 = 40
\]
This means that the contraption is dropped from a height of 40 feet, which represents the height of the school’s roof.
2. **Shape of the Graph**: The graph of this equation is a downward opening parabola, indicating that the height (y) decreases over time (t) as the contraption falls due to gravity.
3. **Maximum Height**: The maximum height is reached when \( t = 0 \) (before the drop starts), which confirms that the initial height of the school's roof is 40 feet.
4. **Impact Point**: As \( t \) increases, the value of \( y \) decreases until it reaches zero, at which point the contraption has hit the ground.
In summary, the correct interpretation of the height of the school's roof is that it is 40 feet high, as given by the equation when \( t = 0 \).
To interpret this situation:
1. **Initial Height**: When \( t = 0 \), the height \( y \) is:
\[
y = -16(0)^2 + 40 = 40
\]
This means that the contraption is dropped from a height of 40 feet, which represents the height of the school’s roof.
2. **Shape of the Graph**: The graph of this equation is a downward opening parabola, indicating that the height (y) decreases over time (t) as the contraption falls due to gravity.
3. **Maximum Height**: The maximum height is reached when \( t = 0 \) (before the drop starts), which confirms that the initial height of the school's roof is 40 feet.
4. **Impact Point**: As \( t \) increases, the value of \( y \) decreases until it reaches zero, at which point the contraption has hit the ground.
In summary, the correct interpretation of the height of the school's roof is that it is 40 feet high, as given by the equation when \( t = 0 \).