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

Question

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?

Answer 1

We have a quadratic of   h(t) = -4t² - 20t

We need to find out when h(t) will be 25 ft

 

-4t² -20t = 25

-4t² - 20t - 25 = 0

 

Look at the quadratic as given.  This will never reach a positive height at all because every term

will be negative.  There is a problem with the equation as given.  Let's work it out to verify.

 

From quadratic equation we have   t = 20/2(-4) ± √[(-20)²-4(-4)(-25))/2(-4)

                                                   = -5/2 ± [√(400-400)]/(-8)

                                                  = -5/2 ± 0

 t = - 5/2 seconds or - 2.5 seconds

 

You need to check your original equation of h = -4t² - 20t

I would bet this should be -4t² + 20t 

 

If this is so then the discriminant is still zero and our answer becomes t = 2.5 seconds