The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted down 5 units and to the left 4 units. What is its equation?
following the translation stated, its equation must be
F(x) = (x+4)^2 - 5
To find the equation of the shifted graph, we first need to start with the basic form of the function, which is G(x) = x^2.
The given information tells us that the graph has been shifted down 5 units and to the left 4 units compared to the standard graph of G(x) = x^2.
To shift the graph down 5 units, we subtract 5 from the function:
F(x) = G(x) - 5
To shift the graph to the left 4 units, we substitute x with (x + 4) in the equation:
F(x + 4) = G(x) - 5
Combining the two shifts, the equation of the shifted graph is:
F(x + 4) = (x + 4)^2 - 5
This equation represents the function F(x) that corresponds to the given graph.