I'm having a difficult time finding inverse functions for polynomials. I know I'm close.

Find the inverse function for:
h(t)=-5t^2+10t+2

Rewrite:
h=-5t^2+10t+2

Swap variables:
t=-5h^2+10h+2

Solve for h:
5h^2-10h=2-t
5(h^2-2h)=2-t
h^2-2h=(2-t)/5
h(h-2)=(2-t)/5

And this is where I'm stuck.

Question

I'm having a difficult time finding inverse functions for polynomials.  I know I'm close.

Find the inverse function for:
h(t)=-5t^2+10t+2

Rewrite:
h=-5t^2+10t+2

Swap variables:
t=-5h^2+10h+2

Solve for h:
5h^2-10h=2-t
5(h^2-2h)=2-t
h^2-2h=(2-t)/5
h(h-2)=(2-t)/5

And this is where I'm stuck.

radar · Answer

It looks like you were going the right direction.  Lets go to the next to last line of your post.:$$h ^{2}-2h =(2-t)/5$$ Now I would use the "completing the square" method to solve this;$$h ^{2}-2h +1 = (2-5)/5 + 5/5 = (7-t)/5$$ Notice that I added a "1" to the left hand side to make that a perfect square, but I had to also add a 1 or 5/5 to the right hand side to maintain the equality.  I further simplified the right hand side.
You now must take the square root of both sides.  This gives you:$$h-1 =\sqrt{(7-t)/5}$$ I am sure you can now take this from here and solve.

anonymous · Answer

Awesome... thanks!

radar · Answer

You're welcome, good luck with your studies.