When graphing a parabola, sometimes it's confusing which way the parabola opens. Does it open up, down, left or right?
A parabola in the form y = x^2 will open up. For every value of y, there will be 2 values for x.
When x = 3, y = 9.
x = -3, y = 9
x = 2, y = 4
x = -2, y = 4
No matter what value you substitute for x, you will get a positive value for y.
If you plot these points in a graph you will notice the graph is symmetric about the y axis. This means the y axis cuts the parabola in half, mirror images on both sides of the axis.
The graph opens down if in the form -y = x^2. This is because all the values which were positive before become negative.
You can also think of the parabola opening towards the linear term. In this case, the linear term is y and the parabola opens up or down, and the y axis runs vertically.
The exact opposite argument is true for parabolas in the form x = y^2 or -x = y^2. In this case the x axis is the axis of symmetry and the parabolas open either right or left (horizontally) and the x axis is the horizontal axis.