please help me and explain to me how you got the answer, pls don’t just say the answer explain how. will mark brainliest if you get it right!

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.

answer: i think it is (1,-2)