Question

The graph of f(x)=x² was transformed to create a graph g(x)=f(x)-3 Which statement about the graphs is true?

a. The vertex of the graph of g is 3 units to the left of the vertex of the graph of f.
b. The vertex of the graph of g is 3 units to the right of the vertex of the graph of f.
c. The vertex of the graph ot g is 3 units above the vertex of the graph of f.
d. The vertex of the graph of g is 3 units below the vertex of the graph of f.

Answer 1

The graph g(x) is f(x) translated 3 units downward, so the vertex of g is 3 units below the vertex of f. The vertex of the graph of g(x)=f(x)-3 is 3 units below the vertex of the graph of f(x)=x².

Step-by-step explanation:

The transformation of the graph of f(x)=x² to g(x)=f(x)-3 is a vertical shift of the original graph. In this case, the entire graph of f(x)=x² is moved down by 3 units. This does not change the left-right position of the graph, but it does change the up-down position.

The vertex of the parabola, which in the case of f(x)=x² is at the origin (0,0), will also move down by 3 units. Therefore, the correct statement is that the vertex of the graph of g is 3 units below the vertex of the graph of f.

Thus, the correct answer to the stated question is option d: The vertex of the graph of g is 3 units below the vertex of the graph of f.