You can put this solution on YOUR website! I'll answer a part of this.
If x is squared then it opens either up or down
and the coefficient of y is positive it opens up
and the coefficient of y is negative it opens down
if y is squared then it opens right or left
and the coefficient of x is positive it opens right
and the coefficient of x is negative it opens left
Which way does this open?
left y is squared and coefficient of x is negative