When the skier puts equal weight on both skis, the ski edges follow a wide parabola. As the skier leans into a turn, more weight is placed on one edge of each ski. The additional weight causes the parabolic edge of the ski to deflect (bend) into an arc of a circle. The circular arc allows the ski to track a smooth curve in the turn. Watch"The Difference between Shaped Skis and Straight Skis"to get a better idea of how this works.

The following 3 points are on a parabola defining the edge of a ski.

(4,1),(2.0.94),(0,1)

The general form for the equation of a parabola is

Ax2+Bx+C=y

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1. Use thex- andy-values of 1 of the points to build a linear equation with 3 variables:A,B, andC. Record your equation here.
2. Repeat this process with 1 of the other 2 points to build a 2nd linear equation. Record your equation here.
3. Repeat this process with the other point to build a 3rd equation. Record your equation here.
4. Build a matrix equation that represents this system of equations. Record your matrix equation here.
5. Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix. Record your result here.
6. Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.