Question

The depth of water in a channel between two successive low tides can be modeled approximately using a quadratic function of time.
Low tide is at 11:45am and the next one also 0.46m is at 11:30pm. High tide is expected to be 2.16m
I need atleast 1 meter of water to launch the boat, preferably on a rising tide.
Recommend the times for launching my boat successfully.

Answer 1

let x be the time since midnight, and y be the water level. We have

y(11.75) = 0.46
y(23.50) = 0.46
the vertex is thus (17.625,2.16)

Now you have three points, so you can determine the parabola, and you want x where y=1.