What's the transformation of y=(x-3)^2+4?

Question

Which way will the graph move?

Answer 1

Hi, Ana.

The number inside the parentheses with the x tells us the horizontal shift; a -3 means the graph moves to the right 3.

The constant tells us the vertical movement of the graph; the +4 tells us that the graph moves up 4.

Your vertex is now at (3,4).

Not appicable to this case, but a coefficient multiplied by the (x-3) would tell us the vertical stretch of the graph.

Hope this helps!

Answer 2

A very general rule:

If g(x) = f(x-h) + k, then the graph of g(x) is produced by shifting the graph of f(x) by h units right and k units up.

For example, if f(x) = x²then your equation is just y = f(x-3) + 4. So your function is just a shift of y = x² by 3 units right and 4 units up.

Answer 3

It actually depends on the original function.

If the original function is y = x², then y = (x-3)^2 moves y = x² to the right by 3 units, and y = (x-3)^2 + 4 moves y = (x-3)^2 up by 4 units.

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Extention: Redo the problem for y=(2x-3)^2+4.