How to add weights to a animation keyframe

Question

This is the easing formulae which i am using to get the values at given time.

 float SineEaseOut(float currentTime, float startValue, float ChangeInValue, float duration)
    {
        return (float)(ChangeInValue * std::sin((float)currentTime / (float)duration  * (M_PI / 2.0)) + startValue);
    }

This formulae will give a speed curve like this.

I want to apply weights to the second keyframe like in the below image i am able to manipulate the speed curve using a handle.

How can i modify the formulae to get the handle effect.