The graph of f(x) = x2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)? g(x) = (x + 3)2
g(x) = x2 − 3
g(x) = x2 + 3
g(x) = (x − 3)2

g(x) = (x + 3)^2

Step-by-step explanation:

When a function is shifted to the left or right we can think of a change of units, like a new independent variable is used.

If we have a quadratic function

and the graph is shifted 3 units to the left, then we can think of a new unit u that is:

The vertix of this parabola, that happens for u=0, happens for x=-3, as the graph is shifted 3 units to the left.

Then, the relation between u and x is:

We can use this relation in the new graph and replace u as:

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0