n Learning and Teaching Mathematics - When a straight line meets a parabola

Volume 2015, Issue 18
  • ISSN : 1990-6811


In his article about the average gradient between two points in LTM No. 17 (pp. 17-19), Alan Christison points out that when two lines are tangents to a parabola, the gradient at the point on the parabola midway between the two points of tangency is not only equal to the gradient of the straight line joining those points, but is also the average of the gradients at the two points of tangency. This scenario is illustrated in the following diagram.

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