Given:
The height of the swipe card in feet after t seconds is
To find:
The maximum height of the swipe card and the time at which it reaches this height.
Solution:
We have,
Here, leading coefficient is -3, which is negative. It means it is a downward parabola and the vertex of the downward parabola is the point of maximum.
If a quadratic function is , then the vertex is
In the given function, we get
Now,
Putting t=2.5 in the given function, we get
So, the vertex of the given parabola is at (2.5,36.75).
Therefore, the maximum height of the swipe card is 36.75 feet and it reaches this height after 2.5 seconds.