ANSWER
B.
[tex]H(x) = 4 {(x - 5)}^{2} - 18[/tex]
EXPLANATION
The given equation is
[tex]H(x) = 4 {x}^{2} - 16[/tex]
This function is the same as:
[tex]H(x) = 4 {(x - 0)}^{2} - 16[/tex]
This function has its vertex at:
(0,-16).
This function is shifted 5 units to the right and two units down.
The new equation is:
[tex]H(x) = 4 {(x - 0 - 5)}^{2} - 16 - 2[/tex]
Simplify to get:
[tex]H(x) = 4 {(x - 5)}^{2} - 18[/tex]
The correct choice is B.
