6. is this correct? is there anything i could have done better? anything that needs to be added? anything that needs to be taken out?

You are correct, except that 12.72 should be positive, not negative.

max = (140/11, 49/11)

Explanation:

We got the same answer, but I used a different method.

The max point of a parabola is found when its derivative is equal to 0 because the slope at the max point is neither increasing or decreasing.

I just solved for when the derivative is 0 and got

max = (140/11, 49/11)

     or (12.727272, 4.45)

I highly recommend you always leave your answers as a fraction unless they specify you to give a decimal answer. Rounding is never good in math or physic because it could lead to errors in bigger problems.