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Sagot :
We have the expression:
[tex]y=(x-4)^2-4[/tex]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:
[tex]y=(x-4)^2[/tex]Now, we do another translation 4 units down, so the vertex is now located at (-4,-4) and the equation becomes:
[tex]y=(x-4)^2-4[/tex]Then, to graph the equation, we have to apply a translation (-4,-4) to the parent function:

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