Rotate 90 degrees over time with Parabolic Easing.

Questions & Answers
1 
private var rotating = false;

function RotateObject (thisTransform : Transform, degrees : Vector3, seconds : float) {
    if (rotating) return;
    rotating = true;
    var startRotation = thisTransform.rotation;
    var endRotation = thisTransform.rotation * Quaternion.Euler(degrees);
    var t = 0.0;
    //var rate = 1.0/seconds;
    var easeSpeed =  -100;
    var timeHandler = 0;

    while (t < 1.0) {
        timeHandler += Time.deltaTime ;
        var rate = easeSpeed * (timeHandler * timeHandler) + (.5) ;
        //t += Time.deltaTime * rate;
        t += rate;
        thisTransform.rotation = Quaternion.Slerp(startRotation, endRotation, t);
        //print("RATE: " + rate);
        //print("TH: " + timeHandler);
        //print("T: " + Time.deltaTime);
        yield;
    }

    rotating = false;
}

Ive got this all messed up i think it is close but The 

timeHandler += Time.deltaTime ;

will always return zero on the print

The idea would be for the 90 rotation to start slow, ramp up through the middle, then slow back down before resting at its +90 increment resting place.

2

How about

private var rotating = false;

function RotateObject (thisTransform : Transform, degrees : Vector3, seconds : float) {
    if (rotating) return;
    rotating = true;

    var startRotation = thisTransform.rotation;
    var endRotation = thisTransform.rotation * Quaternion.Euler(degrees);
    var t = 0.0;
    var rate = 1.0/seconds;

    while (t < 1.0) {
        t += Time.deltaTime * rate;
        thisTransform.rotation = Quaternion.Slerp(startRotation, endRotation, Mathf.SmoothStep(0.0, 1.0, t));
        yield;
    }

    rotating = false;
}

Forgot to say, the reason your `timeHandler` never goes above 0 is because you defined it as an int, so adding `Time.deltaTime` will do nothing (unless you were getting <= 1 fps).