On a given dive, a platform diver's body follows a path that can be modeled by the equation d = - 4t^2 + 2t + 6, where d represents the diver's distance above the water after t seconds. Use this information to determine how long it will take a diver to reach the water's surface.

t = 1.5 seconds

Step-by-step explanation:

Given that d = - 4t^2 + 2t + 6,

where d = distance above the water and

t = seconds.

Let assume that it's a perfect parabola

At the symmetry

t = - b/2a

Where a = - 4, b = 2

t = - 2/2 (-4)

t = 1/4

To determine how long it will take a diver to reach the water's surface

d = - 4t^2 + 2t + 6

At water surface d = 0

4t^2 - 2t - 6 = 0

Factorizing the above equation leads to

4t^2 + 4t - 6t - 6 = 0

4t (t + 1) - 6 (t + 1) = 0

4t - 6 = 0

4t = 6

t = 6/4 = 3/2 = 1.5 seconds

Since t can't be negative so we ignore the second factor.