Parabolas can have both x-intercepts and y intercepts
As you can see from the picture below, the y-intercept is the point at which the parabola intercepts the y-axis
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.
How to find the x-intercepts
Simply solve the quadratic equation by any of the following methods
- by factoring the quadratic equation
- using the quadratic formula
- completing the square
- or by factoring by grouping
How to find the y-intercept of a parabola
Since the y-intercept marks the point where x =0, all that you have to do is substitute 0 in for x in the parabola's equation.
Interactive Demonstration of the intercepts
Explore the relationship between the x and y intercepts of a parabola and its graph by changing the values of a,b and c of the parabola plotter below
