Nature of the intersection of a straight line and curve

In this video you are introduced to the relationship between the roots of a quadratic equation and the intersection of two graphs.

Tangent to a parabola by considering nature of roots

This example is based on roots of an equation so that a straight line is a tangent to a parabola.


  1. Find the value of k for which the line y = x + k is a tangent to the curve y = x2 – 4x + 5