Question

The height h in feet reached by a dolphin t seconds after breaking the surface of the water is given by the following polynomial.
h = -16t2 + 32t
How long will it take the dolphin to jump out of the water and touch the trainer's hand?

Answer 1

h=-16t^2+32t

Answer 2

Calculus or no?

Answer 3

no

Answer 4

Okay, so you're looking for the vertex of a parabola. (This is where the absolute maximum is)

The vertex is given by:
\[\frac{-b}{2a}\]

Answer 5

Where the standard form is:
\[ax^2 + bx + c\]
So can you see what a and b are?

Answer 6

a is -16^2 and b is 32t ?

Answer 7

-16t^2

Answer 8

Here, you only want the coefficients. Don't worry about the "t".
So a = -16 and b = 32.

So plug that into the -b/2a equation and what do you have?

Answer 9

-32/2(-16)

Answer 10

Yep. And what is that?

Answer 11

-32/32

Answer 12

-32/-32 (don't forget your negative signs)

So what is -32/-32 ??

Answer 13

which is 1

Answer 14

Yep, it will take 1 second for the dolphin to touch the trainer's hand.

Answer 15

woooow.. ha i feel dumb. ha. thanks