Parabola: Tangent Line

The sketch below shows the tangent line to the parabola . First, you can move point anywhere on the parabola. Then show the Secant line. Adjust using the slider. Notice as , the secant line becomes the tangent line. Reinforcing what we learned in class, you can show the y-intercept of the tangent line. Notice, given that the tangent line at will always go through , we can also use these two points to determine the slope: