The GCF of the function is option (C) -4(y^{2} - 3y + 4 is the correct answer.
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The greatest common factor (GCF) of a polynomial is the largest monomial that divides evenly into each term.
For the given situation,
The function is [tex]-4y^2 + 12y - 16[/tex]
The factors of 4 = [tex]1,4[/tex]
The factors of 12 = [tex]4,3[/tex]
The factors of 16 = [tex]4,4[/tex]
In this function, the common factor is 4. So take 4 outside of the function.
⇒ [tex]-4(y^{2} - 3y + 4)[/tex]
Hence we can conclude that the GCF of the function is option (C) -4(y^{2} - 3y + 4) is the correct answer.
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