Question

Which statement is true ? Help plzzzz

Answer 1

Answer:

Correct choice is B

Step-by-step explanation:

The quadratic function g(x) has equation $g(x)=ax^2+bx+c.$ Find values of a, b and c:

$g(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2.$

$g(2)=3=a\cdot 2^2+b\cdot 2++2\Rightarrow 4a+2b=1.$

$g(4)=2=a\cdot 4^2+b\cdot 4+2\Rightarrow 16a+4b=0.$

From the last equation $b=-4a$ and $4a-8a=1,\\ \\a=-\dfrac{1}{4},\\ \\b=1.$

The equation of the quadratic function g(x) is

$g(x)=-\dfrac{1}{4}x^2+x+2.$ 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.