Another Muddy Time in PreCalc

Well. Time has gone on and another problem has entered my life. When coming up with a  quadratic equation when given three random points, I seem to struggle. Sometimes, I combine like terms incorrectly. Other times, I don't keep the signs (+/-) with their proper numbers. Most times, it's a very small mistake that changes the entirety of the equation. What makes it worse, is that I do it correctly on some quizzes or assignments, but incorrectly on others, so I can never really pinpoint exactly what the core of my problem is. Although it seems somewhat easier now, it still trips me up every time and makes me want to rethink my work, even if I previously thought my original answer was correct.