Answer:
Correct choice is B
Step-by-step explanation:
The quadratic function g(x) has equation [tex]g(x)=ax^2+bx+c.[/tex] Find values of a, b and c:
[tex]g(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2.[/tex]
[tex]g(2)=3=a\cdot 2^2+b\cdot 2++2\Rightarrow 4a+2b=1.[/tex]
[tex]g(4)=2=a\cdot 4^2+b\cdot 4+2\Rightarrow 16a+4b=0.[/tex]
From the last equation [tex]b=-4a[/tex] and [tex]4a-8a=1,\\ \\a=-\dfrac{1}{4},\\ \\b=1.[/tex]
The equation of the quadratic function g(x) is
[tex]g(x)=-\dfrac{1}{4}x^2+x+2.[/tex] This quadratic function determines the parabola with vertex at point (3,2). Thus,
1. The maximal value of f(x) is 4 at x=2.
2. The maximal value of g(x) is 3 at x=2.
Thus, the maximal value of f(x) is greater than the maximal value of g(x). So option B is correct.
