How to draw a tangent line at a point on a parabola using the geometric sketchpad

Drawing a tangent line at a point on the parabola in the geometry sketchpad can help us understand the properties of the parabola more intuitively. PHP editor Yuzai will introduce in detail how to use the geometric sketchpad to achieve this operation in this article. By reading the following content, you can master the steps of drawing tangent lines to a parabola and better understand this important mathematical concept.

1. Create a new geometric sketchpad file. Select the [Draw]-[Grid Style]-[Square Grid] command to draw a coordinate system.

2. Select the [Data]-[New Function] command, enter the equation as shown in the figure below, and click [OK].

3. Select the upper left corner of the drawing board to generate the formula, select [Draw] - [Draw New Function] command to generate a parabola,

4 .Keep the parabola selected, select the [Construction]-[Point on Function Image] command, and pick any point A on this parabola. Select this point, select the [Measure]-[Abscissa] command to measure the abscissa value of point A. In the same way, measure the ordinate of this point.

5. Select the parabolic equation, and then select the [Data]-[Define Derivative Function] command, and the first-order derivative function f’(x) will appear.

6. Select the [Data]-[New Function] command, enter the equation, and click [OK].

7. Select the newly generated equation, select the [Draw]-[Draw Function] command to draw the tangent line of point A. as the picture shows. When point A is moved, its tangent will also change accordingly.

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