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

2. Originally Posted by william
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
$y=3x^2 +12x - 7$
To find the inverse , $f^-1(x)$ make a table of values and switch the values of x for the values of y.

3. Originally Posted by william
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:

$y=3x^2+12x-7\implies x=3y^2+12y-7\implies x+7=3(y^2+4y)\implies \tfrac{1}{3}(x+7)=y^2+4y$

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

4. Originally Posted by Chris L T521
To find the inverse, the technique of completing the square is necessary!

I'll start you off:

$y=3x^2+12x-7\implies x=3y^2+12y-7\implies x+7=3(y^2+4y)\implies \tfrac{1}{3}(x+7)=y^2+4y$

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
How exactly do I complete the square and what method did you use?