Your parents will appreciate your apology. You obviously feel guilty so just start by simply saying "I'm Sorry" sometimes that's all that needs to be said. Just say it will sincerity. Your parents will most likely be able to tell that you mean it.
You know it's not a shame if you tell them sorry facing them, instead that's better for you and for them .. because you'll never know how much they love you and they would appreciate your sorry so much and believe me it'd make their day :)
