Answer:
[tex]F(x)=(x-3)^{2}-4[/tex]
Step-by-step explanation:
The graph of F(x) is a translation of the graph of G(x) by 4 units down and 3 units right.
[tex]G(x)=x^{2}[/tex]
4 units down is the vertical shift. Vertical shift is obtained by adding or subtracting a number from the function value. Subtraction indicates a downward shift and addition indicates an upward shift. Since the graph is shifted 4 units down, the new equation after this translation will be:
[tex]x^{2} - 4[/tex]
3 units to the right is the horizontal shift. Horizontal shift is obtained by adding or subtracting a number from x. Subtraction indicates a shift towards right and addition indicates a shift towards left. Since the graph is being shifted 3 units to right, the new equation after this transformation will be:
[tex]F(x)=(x-3)^{2}-4[/tex]
