Answer
$${\text{parabola}}$$
Work Step by Step
$$\eqalign{
& y = 2{x^2} + 3x - 4 \cr
& {\text{Add 4 to both sides}} \cr
& y + 4 = 2{x^2} + 3x \cr
& {\text{Complete the square and factor}} \cr
& y + 4 - \frac{9}{2} = 2\left( {{x^2} + \frac{3}{2}x + \frac{9}{4}} \right) - \frac{9}{2} \cr
& y - \frac{1}{2} = 2{\left( {x + \frac{3}{2}} \right)^2} - \frac{9}{2} \cr
& y + 4 = 2{\left( {x + \frac{3}{2}} \right)^2} \cr
& {\left( {x + \frac{3}{2}} \right)^2} = \frac{1}{2}\left( {y + 4} \right) \cr
& {\text{The equation is written in the form }}{\left( {x - h} \right)^2} = 4p\left( {y - k} \right) \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation }}y = 2{x^2} + 3x - 4{\text{ is a parabola}} \cr} $$
