please help me!! :(

Question

On a windy morning, a hot air balloon starts rising and flying away from the top of a hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the hill, can be modeled by this function:

h(x) = –16x2 + 64x + 80.

The balloon will reach its maximum height after how many hours?

Answer 1

The equation h(x) = -16x² + 64x + 80 when graphed will be a parabola opening down. This means that the max height will be at its' vertex. The "x" value (hours) of the vertex can be determined by the formula x = -b/2a where b = 64 and a = -16: x = -64/2(-16)--->x = -64/-32--->x = 2. Therefore, the balloon will reach its' max height 2 hours after it starts its' ascent.

Hope this helps!

Answer 2

In the function (parabola) h(x) = -ax² + bx + c

The maximum always occurs at x = -b / 2a

In this case x = -64 / 2(-16), or x = 2

Answer 3

There is a quick and easy way to find the answer.....please see the attached video. Enjoy!!! If you have questions, simply add comments accordingly.