Question

If a ball is thrown upward from the ground with an initial speed of 64 feet per second, its height h, infeet, after t seconds is-1672 +642-h = -16+2 +64t.What is the maximum height the ball

Answer 1

Maximum value of a quadratic function

Given a quadratic function in the form:

`f(x)=ax^2+bx+c`

The maximum or minimum value of the function occurs at the vertex of the parabola that represents the function.

The x-coordinate of the parabola is given by:

`x_m=-(b)/(2a)`

If a is positive, then the function has a minimum value, if a is negative, then the function has a maximum value.

The height of a ball h after t seconds is given by:

`h=-16t^2+64t`

This is a quadratic function with a=-16, b=64, c=0

The time where the ball reaches its maximum height is:

`t=-(b)/(2a)=-(64)/(2(-16))=2\sec`

Now we substitute this value in the function:

`h=-16\cdot2^2+64\cdot2=-64+128=64ft`

The maximum height of the ball is 64 ft