The graph of the quadratic function y 2x24x 1 is pictured below along with the point P 1 7 on the parabola and the tangent line through P A line that is tangent to a parabola does not Intersect the parabola at any other point We can use this fact to find the equation of the tangent line a If m is the slope of the tangent line then using the slope point formula the equation of the tangent line will be y m x b The values of x for which the point x y lies on both the line and the parabola satisfy the quadratic equation 2x bx c 0 where be and c b and c should depend on m c For most values of m the quadratic equation in part b has two solutions or no solutions The value of m for which the quadratic equation has exactly one solution is the slope of the tangent line This value is ma