Final answer:
A Bézier curve is defined by a parametric equation and the given problem involves control points for a cubic Bézier curve. This cannot be expressed as a single algebraic equation but requires evaluating the parametric equations using the provided control points.
Step-by-step explanation:
In mathematics, a Bézier curve is a parametric curve frequently used in computer graphics and related fields. The curve, defined by a set of control points, can be of any degree, with the degree determined by the number of control points minus one. A cubic Bézier curve, which is of third degree, is determined by four control points.
The equation for a cubic Bézier curve with control points P0, P1, P2, and P3 is given by:
B(t) = (1 - t)^3 * P0 + 3 * (1 - t)^2 * t * P1 + 3 * (1 - t) * t^2 * P2 + t^3 * P3
where t ranges from 0 to 1. For the given control points (-2, -2), (3, 9), (5, 4), and (11, 10), you would plug these into the equation as P0, P1, P2, and P3 respectively.
Unfortunately, we cannot provide a simple algebraic equation for the Bézier curve as it is a parametric expression and not a standard polynomial function. Computing specific points on the curve involves substituting values of t into the Bézier equation.