Maximizing Plant Height Using Quadratics

A gardener is observing the growth of a particular plant species over time. The growth can be modeled by a quadratic function, given by the equation:

$$ h(t) = -2t^2 + 8t + 4 $$

where $h(t)$ represents the height of the plant in centimeters, and $t$ represents the time in weeks. The gardener wants to determine the time at which the plant reaches its maximum height.

To find this, you need to calculate the value of $t$ that maximizes the function. Once you find this time, calculate the maximum height of the plant at that time. Enter your answer to the nearest hundredth.