Question

Graph the equation shown below by transforming the given graph of the parent function.y=(x-4)²-4

Answer 1

We have the expression:

`y=(x-4)^2-4`

The parent function is the quadratic parent function: y=x^2.

If we start with y=x^2, and we translate the graph 4 units to the left, we translate the axis of symmetry, that was at x=0 in the parent function, to x=-4, so it corresponds to the equation:

`y=(x-4)^2`

Now, we do another translation 4 units down, so the vertex is now located at (-4,-4) and the equation becomes:

`y=(x-4)^2-4`

Then, to graph the equation, we have to apply a translation (-4,-4) to the parent function: