Is the Gateway Arch a Parabola?
- Roy Wright
The three red points shown below can be moved, to allow you to attempt to find a quadratic polynomial that "fits" the shape of the Gateway Arch in St. Louis, Missouri.
Because of the shape of the Arch (moving downward to the left and to the right) it makes sense that an even-degree polynomial with a negative leading coefficient should be used to describe that shape. But as it turns out, the graph of a quadratic polynomial function cannot nearly capture the true shape of the Arch. In reality, the exact shape of the Arch comes from a more advanced function than those that we deal with in an algebra course, but as a scientist or engineer might tell you, polynomials can be indispensable in approximating just about any smooth shape. Use the red slider to change the degree; experiment with a fourth-degree (AKA "quartic") polynomial, which can be determined by five points.