Final answer:
To express the curve described by x(t) = t² and y(t) = 2t + 1 in terms of x and y, eliminate the parameter t. This results in the parabolic equation y = 2(√ x) + 1.
Step-by-step explanation:
The curve described by the parametric equations x(t) = t² and y(t) = 2t + 1 can be expressed by an equation in x and y by eliminating the parameter t. Since x is given by t², we can solve for t by taking the square root of x (keeping in mind that t could be positive or negative, but we'll assume t ≥ 0 for this problem). We get t = √ x.
Substituting this into the second equation, we have y = 2(√ x) + 1. This equation represents a parabola in the x-y coordinate system. When graphing such a curve, one typically calculates a series of x and y pairs, then plots these points on a graph to visualize the parabola.