If the graph of the function f(x)=x² is translated 3 units up and 1 unit left the resulting function of g(x) will become g(x) = (x+1)² + 3. See the attached graph.
The original graph of f(x)=x² is a standard parabola centered at the origin, opening upwards. When transformed tog(x) = (x+1)² + 3, the graph shifts one unit to the left and three units up.
The vertex, originally at (0, 0), now becomes (-1, 3). The parabola maintains its upward orientation but is repositioned in the coordinate plane.
Both graphs share the same shape, but the translated graph reflects changes in its position, reflecting the impact of the translation on the original quadratic function.