The graph of the quadratic function y = 2x2 4x + 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^2 + bx + c = 0 where b= ... 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 m= ...