Question

okay it says Write the function whose graph is the graph of y = x^2, but is shifted to the left 4 units

i answered y = x^2 - 4 but i got it incorrect

Answer 1

To shift to the left or right, you need to alter X. In Y = X^2 - 4 you have altered Y and thus the graph has gone down 4 units

You can check it this way,
In the original graph, For X = 0, Y was equal to 0.
But in the equation Y = X^2 - 4, when X = 0, Y = -4.

You can see that the Y coordinate shifted downwards, so the entire graph shifted downwards.

To move it to the left, you have to add the distance to X

So the equation becomes

Y = (X + 4)^2

Now to check if graph has shifted left or right, we fix the value of Y and find corresponding value of X for both graphs.

In Y = X^2, when Y = 0, X = 0.
In Y = (X + 4)^2, when Y = 0, X = -4.

Hence you can see that the X coordinate was shifted by 4 units to the left. Thus the whole graph was shifted 4 units to the left.
Hence the correct answer is

Y = (X + 4)^2