# How do you identity if the equation 2x^2+3x-4y+2=0 is a parabola, circle, ellipse, or hyperbola and how do you graph it?

Feb 23, 2017

The given equation is a Parabola.

#### Explanation:

Given -

$2 {x}^{2} + 3 x - 4 y + 2 = 0$

The general for of the conic equation can be written as

$A {x}^{2} + C {y}^{2} + D x + E y + F = 0$

In such case -

If $A \times C = 0$then it is a parabola.

In the given equation ${y}^{2}$ is absent. Hence its coefficient is $C = 0$

The coefficeint of ${x}^{2}$ is $A = 2$

In the given equation $A \times C = 0$. Hence the given equation is a Parabola.

To graph the equation, solve it for $y$

$4 y = 2 {x}^{2} + 3 x + 2$
$y = 0.5 {x}^{2} + 0.75 x + 0.5$

Find its vertex

$x = \frac{- b}{2 a} = \frac{- 0.75}{2 \times 0.5} = - 0.75$

Take a few points on either side of $x = - 0.75$
Calculate the corresponding $y$ values

Tabulate them

Plot the point on a graph sheet. connect them with a smooth curve.