SOLUTION: In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface w

Question 981452: In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface water will the dolphin reach 25 feet to get the fish from the trainer's hand?
Found 3 solutions by macston, Boreal, Alan3354:
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
.

.
For h=25 feet:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=800 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.03553390593274, -1.03553390593274. Here's your graph:

.
So t=6.04 seconds.
.
ANSWER: The dolphin gets the fish 6.04 seconds after breaking water.
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
h=25=-4t^2-20t;I think this has to be -4t^2+20t, because otherwise as t increases from zero, the height gets less and less.
4t^2-20t+25=0; if I move everything to the left side.
(2t-5)^2=0
2t=5
t=2.5 seconds. NOTE: if I use the equation given with -20t, I get t=-2.5 seconds
-4(2.5)^2+20(2.5)=-25+50=25
2.5 seconds

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
In a dolphin show, the height h in feet reached by a dolphin t seconds after breaking the surface water is given by h=-4t^2 - 20t.Find how many seconds after breaking the surface water will the dolphin reach 25 feet to get the fish from the trainer's hand?
=====================
h(t) = -4t^2 - 20t = 25
That won't work.
It's h(t) = -4t^2 + 20t = 25
The 20 is its vertical speed when it leaves the water and becomes a projectile.
-4t^2 = 20t - 25 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=0 is zero! That means that there is only one solution: .
Expression can be factored:

Again, the answer is: 2.5, 2.5. Here's your graph:

=============
t = 2.5 seconds.

RELATED QUESTIONS
How do you solve: The height h in feet reached by a dolphin t seconds after breaking... (answered by nerdybill)
In a pool at a water park, a dolphin jumps out of the water traveling at 20 feet per... (answered by ankor@dixie-net.com)
A dolphin jumps from the water at an initial velocity. The equation h=-16t^2+80t models... (answered by ikleyn)
{{{ h(t) = c - (d-4t)^2 }}} At time t=0, a ball was thrown upward from an initial... (answered by ikleyn)
h(t)=c-(d-4t)(d-4t) At time t=0, a ball was thrown upward from an initial height of 6... (answered by richwmiller)
Please help. Tim kicks a ball off the ground. After t seconds, its height, h (in... (answered by stanbon)
Tim kicks a ball off the ground. After t seconds, its height, h (in feet), is given by... (answered by Greenfinch)
h(t)= c-(d-4t)^2 At time t=0, a ball was thrown upward from an initial height of 6... (answered by solver91311)
the height in feet reached by a batted baeball after t seconds is given by... (answered by nerdybill)