Question 643090
the graph below shows the original equation and its inverse.
{{{graph(600,600,-10,10,-10,10,x^2+2x+6,-1+sqrt(x-5),-1-sqrt(x-5),x)}}}
the inverse equation is found as follows:
start with:
y = x^2 + 2x + 6
subtract 6 from both sides of the equation to get:
x^2 + 2x = y - 6
complete the squares on the left side of the equation to get:
(x+1)^2 = y - 6 + 1 which becomes:
(x+1)^2 = y - 5
take the square root of both sides of the equation to get:
x+1 = +/- sqrt(y-5)
+/- means plus or minus
subtract 1 from both sides of the equation to get:
x = -1 +/- sqrt(y-5)
replace x with y and y with x to get:
y = -1 +/- sqrt(x-5)
that's your inverse equation as seen on the graph.