Find Points Of Intersection of Parabola and Line - Calculator

A calculator to find the points of intersection of a parabola and a line.

Intersection of a Parabola and a Line

The equation of the parabola is of the form
y = a x2 + bx + c
and the equation of the line is of the slope intercept form
y = m x + B
If y = m x + B is substituted into y = a x2 + bx + c, we end up with a quadratic equation given by:
m*x + B = a x
2 + bx + c
To find the points of intersection, this calculator solves the above equation to find the x coordinates and then uses equation y = m x + B to find the y coordinates.

How to Use the Calculator

1 - Enter the coefficients a,b and c then enter the slope of the line m and its y intercept B and then press "enter". The x and y coordinates of the two points of intersection P1 and P2 are displayed.
Note that this problem may have two points of intersection, one point of intersection or no points of intersection.


a =
, b = , c =

m =
, B =
Decimal places =

Coordinates of the points of intersection

P1( , )

P2( , )

More References and Links

Find the Points of Intersection of a Parabola with a Line. Another tutorial on finding the points of intersection of a parabola with a line; general analytical solution.
Maths Calculators and Solvers.