Eliminate the parameter in $x = t^2 + 3 t$ and $y = t - 2$ and then identify the parametric curve and sketch its image in the $xy$-plane on a piece of paper.

Equation:
Image in the $xy$-plane: Choose Circle Semicircle opening up Semicircle opening down Semicircle opening right Semicircle opening left Ellipse Ellipse opening up Ellipse opening down Ellipse opening right Ellipse opening left Hyperbola opening up Hyperbola opening down Hyperbola opening right Hyperbola opening left Parabola opening up Parabola opening down Parabola opening right Parabola opening left