Answer to Question #137928 in Analytic Geometry for Rhea Marzan

Question

Draw the parabola with the equation: 4x

2 + 6x − 3y = 4.

Answer 1

Given equation is

$4x^2+6x-3y=4$

$4(x^2+\frac{3}{2}x)-3y=4$

$4(x^2+\frac{3}{2}x+\frac{9}{16}-\frac{9}{16})-3y=4$

$4(x+\frac{3}{4})^2-\frac{9}{4}-3y=4$

$4(x+\frac{3}{4})^2=3y+4+\frac{9}{4}$

$4(x+\frac{3}{4})^2=3y+\frac{25}{4}$

at x=0, $4\times \frac{9}{16}=3y+\frac{25}{4}$

$3y=\frac{9}{4}-\frac{25}{4}$

$3y=\frac{-16}{4}$

3y=-4

y=-1.33

At y=0,

$4(x+\frac{3}{4})^2=\frac{25}{4}$ ,$(x+\frac{3}{4})^2=\frac{25}{16}$ ,$(x+\frac{3}{4})=\pm\frac{5}{4}$

$we get x=\frac{1}{2}$ and $-2$

our parabola must pass through (0.5,0),(-2,0) and (0,-1.33)

The parabola is