For high school Mathematics Pre-Specialist, I have been given the task of writing a mathematical investigation based on the following three questions:
Quadratic Bezier curve enables a smooth curve to be drawn through two points . In the example that you have considered the smooth curve passed through points A and C with point B being the control point that determines the shape of the curve. The parametric equations for these bezier curves will be quadratics (ie they involve the parameter squared) 1. Draw at least 3 Bézier curves for different positions of the control point B using the same end points A (-3,4) and C (4,-6) and include the curves in your report. • Show how the parametric equations for these curves were developed. • What properties do all of these curves have in common? • Explain how the position of the control point changes the shape of the curve. A Quadratic Beziér curve can be used to construct a smooth curve to connect two line segments, in this case the control point will be the intersection point of the two line segments extended. 2. Sketch the line segments given below • AB y=2x+1 0
Since we have been studying Vectors and this Bézier Curve assignment is merely a side project, I have no idea how to complete it. The questions appear to make sense, so my biggest problem is likely to be drawing a Bézier Curve through, say, two points. I've been trying to do this in Geogebra, but to no avail. How can it be done?