calculus

The parametrization to describe the left half of the parabola is x = t, y = t^2 - 4t + 3, where t < 2. This parametrization describes the parabola by starting at the vertex, (2, 3), and then moving along the parabola in the left direction as the parameter t decreases from 2 towards 0. As t decreases, the x-coordinate decreases, with the y-coordinate according to the equation of the parabola. Thus for each subsequent decrease in the value of t, the point on the parabola descends a certain amount in the negative y-direction and moves to the left a certain amount in the negative x-direction as determined by the equation of the parabola.