Parabolas can have both x-intercepts and y intercepts

y-intercept
- As you can see from the picture below, the y-intercept is the point at which the parabola intercepts the y-axis

x-intercepts
The x-intercepts are the points or the point at which the parabola intersects the x-axis. A parabola can have either 2,1 or zero real x intercepts.

x-intercepts in greater depth

A parabola can have 2 x-intercepts, 1 x-intercept or zero real x intercepts. If the parabola only has 1 x-intercept (see middle of picture below), then the parabola is said to be tangent to the x-axis.