Question 65295
Since the equation for the depth as a function of time is a parabola that opens downward ({{{-t^2}}}), the vertex of the parabola occurs at the maximum value of the independent variable, t.
The t-coordinate of the vertex can be found by: {{{t = (-b)/2a}}} where: b = 10 and a = -1.
{{{t = (-10)/2(-1)}}}
{{{t = 5}}}
The maximum depth, D, occurs at t = 5 or 5 hours.
To find the value of D at this time, substitute t=5 into the original equation and solve for D.
{{{D = -(5)^2 + 10(5)}}}
{{{D = -25+50}}}
{{{D = 25}}}
The maximum depth is 25 feet(?).