Given the quadratic y = 3x2 + 12x - 7, find the inverse of the quadratic. Graph both the original function and the inverse on the same set of axes. State the domain and range of both
To find the inverse, the technique of completing the square is necessary!
I'll start you off:
$\displaystyle y=3x^2+12x-7\implies x=3y^2+12y-7\implies x+7=3(y^2+4y)\implies \tfrac{1}{3}(x+7)=y^2+4y$
Try to take it from here.
Now, here's the graph of the functions:
(The functions are inverses, since are reflections about the line y=x [in green])
--Chris