what is the inverse of y=2x^2 +8x+3 ??

help me please!

Question

what is the inverse of y=2x^2 +8x+3 ??

help me please!

agent0smith · Answer

It won't have a real inverse, since an x^2 function is not invertible as it's not one-to-one.

anonymous · Answer

http://www.wolframalpha.com/input/?i=inverse+of+f%28x%29%3D2x^2+%2B8x%2B3

agent0smith · Answer

You can invert it by completing the square (this is also how the quadratic formula is derived)

anonymous · Answer

i am confused can you give me an example?

agent0smith · Answer

But it's still not a technical inverse, since parabolas are not one-to-one functions

anonymous · Answer

um.. what if the function is restricted?

anonymous · Answer

to one to one function

agent0smith · Answer

Yes, you can restrict it to one-to-one. To complete the square:
$$y=2x^2 +8x+3 $$
$$y=2(x^2 +4x)+3$$ subtract 8 in this next step, since we added 8 from the parentheses: $$y=2(x +2)^2+3-8$$
$$y=2(x +2)^2-5$$

agent0smith · Answer

Now try rearranging that to solve for x.

anonymous · Answer

I see what is happening now! thank you :)

agent0smith · Answer

Good :)
$$y=2(x +2)^2-5 $$ just rearrange it until you have x = ....$$y+5=2(x +2)^2$$

anonymous · Answer

yeh!! it is clearer thank you so much for your help :)

agent0smith · Answer

And then swap the y with x and x with y.

agent0smith · Answer

@rizwan_uet wolframalphas inverse appears to be wrong... looks like it should be $$-2 ± \sqrt \frac{ x+5 }{ 2 }$$

agent0smith · Answer

Their graph is correct, but the equation wolfram has is not.

anonymous · Answer

@agent0smith wow