# Math Help - More Inverse...

1. ## More Inverse...

I'm sorry I have to keep pestering everyone about inverse. I ran into a problem on my homework that is frustrating me. I still kind of don't get it.... If anyone could put it put it step by step it would be greatly appreciated.

Find the Inverse: y= 2x^2 + 6x - 4

2. To do this you need to isolate x then switch y for x and vice versa. So let's isolate x:

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

$y=2(x^2+3x)-4$

$y=2(x^2+3x+\frac{9}{4}-\frac{9}{4})-4$ (complete the square: 3 divided by 2 squared)

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

$y=2(x+\frac{3}{2})^2-\frac{17}{2}$

$\frac{1}{2}(y+\frac{17}{2})=(x+\frac{3}{2})^2$

$x=\sqrt{\frac{1}{2}(y+\frac{17}{2})}-\frac{3}{2}$

So then the inverse of y is $y^{-1}(x)=\sqrt{\frac{1}{2}(x+\frac{17}{2})}-\frac{3}{2}$