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6/6 6. 2/5 points | Previous Answers The graph of the quadratic function y = 2 x 2 – 4 x + 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- $$−1 ) + $$7 (b) The values of x for which the point (x,y) lies on both the line and the parabola satisfy the quadratic equation: 2 x 2 + bx + c = 0 where b= $$12 and c= $$12 (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 = $$−3 .

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