Function f is represented by the equation given below.

function g has a vertex at (2,4) and the parabola opens downwards.

which of the following statements is true? f(x)=x^2-5x+6

a.
the minimum of function f is at (-5,6).
b.
the minimum of function g is at (2,4).
c.
the y-intercept of function f is less than the y-intercept of function g.
d.
the y-intercept of function f is greater than the y-intercept of function g.

Step-by-step explanation:

Unfortunately, you have not shared function g(x).  But I can focus on questions involving function f(x) alone:

A:  We can find the x-coordinate of the minimum of f by calculating x = -b/(2a).  Here that comes out to x = 5/2*1) = 5/2.  This does not agree with A.  A is FALSE.

B:  Function g(x) unknown; cannot answer this.

C:  The y-intercept of function f(x) is 6.  That of g(x) is unknown.

D:  The y-intercept of function f(x) is 6.  That of g(x) is unknown

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."