Question

Could someone show me step by step in how to find the zeros to this function? y = 1/(x+2)(x-2) +2 (Vertical translation 2 up)

Answer 1

\[y=\frac{ 1 }{ (x+2)(x-2) }+2\]

Answer 2

We want \(y=0\):\[
0=\frac{1}{(x+2)(x-2)}+2
\]Multiply both sides by \((x+2)(x-2)\).\[
0=1+2(x+2)(x-2)
\]This expands into a quadratic.

Answer 3

One thing to note, is that we know \(x\neq 2\) and \(x\neq -2\), because the function is undefined at those points. This restriction is still true even if our equation does not show it.