Question

The graph of f(x) = x^2+ 3 is translated to produce the graph

of g(x) = (x + 2)^2+ 3. In which direction was the graph of f
translated?
left
right
up
down

Answer 1

the graph of f(x) is translated 2 units to the LEFT

Explanation:

The original function, f(x) = x^2 + 3, has its vertex at (0, 3). If we translate the graph h units to the right, this function becomes g(x) = (x - h)^2 + 3. The x-coordinate of the vertex appears h units to the right of the original vertex.

In this case g(x) = (x + 2)^2 + 3, which tells us that h = -2. The effect of inserting the "-2" is that the graph of f(x) is translated 2 units to the LEFT.

If, on the other hand, we went from f(x) = x^2 + 3 to g(x) = (x - 2)^2 + 3, the original graph would be translated 2 units to the right.