1. ## Parabola Graph

I'm having trouble graphing the parabola $\displaystyle y^2 +2y +12x+25=0$.

I rearrange and factor: $\displaystyle (y+1)^2=12x-26$. This isn't really the form $\displaystyle y^2=4Px$ because of the extra constant. Is the parabola just a transformation of $\displaystyle y=12x$? I'm not nsure how to graph this.

Edit:$\displaystyle (y+1)^2=-12x-24$

2. $\displaystyle y^2 +2y +12x+25=0$

$\displaystyle (y^2 +2y +1)-1+12x+25=0$

$\displaystyle (y^2 +2y +1)+12x+24=0$

$\displaystyle (y+1)^2+12x+24=0$

$\displaystyle (y+1)^2=-2x-24$

$\displaystyle y+1=\pm\sqrt{-2x-24}$

$\displaystyle y=\pm\sqrt{-2x-24}-1$

What kind of parabola is this?

3. Originally Posted by pickslides
$\displaystyle y^2 +2y +12x+25=0$

$\displaystyle (y^2 +2y +1)-1+12x+25=0$

$\displaystyle (y^2 +2y +1)+12x+24=0$

$\displaystyle (y+1)^2+12x+24=0$

$\displaystyle (y+1)^2=-2x-24$

$\displaystyle y+1=\pm\sqrt{-2x-24}$

$\displaystyle y=\pm\sqrt{-2x-24}-1$

What kind of parabola is this?

You made an error: , it should be $\displaystyle -12x-24$

I finally figured it out. The equation can be factored $\displaystyle (y+1)^2=-12(x-2)$ This is just a transformation of the parabola $\displaystyle y^2=-12x$ which can be written as $\displaystyle x=-\frac{1}{12}y^2$. So it is a parabola where the x-axis is the axis of symmetry. In other words, it's sideways.