3. A water balloon was thrown from a window. The height
of the water balloon over
time can be modeled by the
function y= 16x2 + 160x + 50.
What was the maximum
height of the water balloon
after it was thrown?

Note: It the given equation the coefficient of must be -16 instead of 16.

Given:

Consider the height  of the water balloon over  time can be modeled by the  function

To find:

The maximum height of the water balloon  after it was thrown.

Solution:

We have,

Here, leading coefficient is negative. So, it is a downward parabola and vertex of a downward parabola, is the point of maxima.

If a parabola is , then

Here, . So,

Now, put x=5 in the given equation.

The vertex of the given parabolic equation is (5,450).

Therefore, the maximum height of the balloon is 450 units after 5 units of time.