The number that belongs to the blank is 16
Explanation:
The given function is f(x) = 3(x² − 8x + ____) + 9
We need to determine the number that belongs to the blank.
The number can be determined by completing the square.
The middle term is 8
The last term can be determined by dividing the middle term by 2 and then squaring the term.
Thus, we have,
[tex]\frac{8}{2}=4[/tex]
Squaring the term, we get,
[tex]4^2=16[/tex]
Thus, the number that belongs to the blank is 16.
