ANSWER
[tex]f(x) = 4 {(x - 7)}^{2} - 19[/tex]
EXPLANATION
The given equation is
[tex]g(x) = 4 {x}^{2} - 16[/tex]
If the equation is shifted 7 units to the right and 3 units down, then the new equation becomes.
[tex]f(x) = g(x - 7) - 3[/tex]
This implies that,
[tex]f(x) = 4 {(x - 7)}^{2} - 16 - 3[/tex]
The required equation is
[tex]f(x) = 4 {(x - 7)}^{2} - 19[/tex]
