Final answer:
The transformation of f(x) = x² to f(x) = (x-1)² + 3 involves a horizontal shift right by 1 unit and a vertical shift up by 3 units, moving the vertex to (1,3). To graph, translate the standard parabola accordingly, labeling with f(x) and x, and scaling the axes to fit the graph.
Step-by-step explanation:
The transformation of the parent function f(x) = x² into f(x) = (x-1)² + 3 can be described as follows: first, the graph of f(x) = x² is horizontally translated 1 unit to the right because of the (x-1) term.
This shift moves the vertex of the parabola from the origin (0,0) to the point (1,0). Then, the whole graph is translated vertically upwards by 3 units due to the '+3' at the end of the function, which moves the vertex to the final position of (1,3).
To graph this transformed function, we would start with a standard parabola that opens upwards. Then we would shift the parabola 1 unit to the right (making the line of symmetry x=1 instead of x=0) and 3 units up, giving it a new vertex at (1,3).
Then you would scale the x and y axes and label the graph with f(x) and x, making sure to adjust the scales to include the maximum x and y values you plan to show on your graph.