Picture of Parabola Intercepts

Parabola Intercepts

x-intercept and y-intercept of a Parabola

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

Picture of Y intercept of Parabola Graph
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.

Picture of the x-intercepts of a parabola

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.

Image of x intercept graphs

How to find the x-intercepts

Simply solve the quadratic equation by any of the following methods

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

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