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

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:

View image KeariC415587
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