Help me plz on a post test

For the given quadratic equation convert into vertex form, find the vertex and find the value for x=6 y=-2x^2+2x+2

Cassie is traveling 675 miles today to visit her brother and his family. so far, she has stopped for gas three times. at the first stop, she put in 7.1 gallons of gas and paid $23.79. at her second stop, she put in 5.8 gallons of gas and paid $19.08. and, at the third stop, 6.6 gallons and paid $20.39. at which stop did casey pay the most for gas?

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is