A height model in vertex form has a squared part that reaches at its turning point. A negative coefficient makes every nonzero square lower the output, so the maximum is the output when the square is zero. The input at the peak tells you when it happens, not how high the object goes.
Hints
- Hint 1
In vertex form, the turning point occurs when the squared part is . What value of makes equal ? Remember that measures seconds, not meters.
- Hint 2
A square is nonnegative, meaning it is at least . Multiplying it by makes that term at most . When will that term stop lowering the drone’s height?
Step-by-step
Read the peak from vertex form
Step 1Find when the squared part is zero
No Desmos needed. The model is already in vertex form, which shows the turning time. The squared part is when its inside is :
Add to find the time:
That is seconds after takeoff, not a height.
- Step 2
Check that this time gives a maximum
Any square is at least . Multiply by the negative coefficient , which flips the inequality:
At , this term is ; at every other time, it lowers the height. So the turning point is a maximum, not a minimum.
- Step 3
Find the height at that time
Substitute into the height model:
The product is , so:
The drone’s maximum height is meters. Choice B.