Parabola Intercepts

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.

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