Answer:
B. is greater than
Step-by-step explanation:
As the graph of function f(x) is a parabola, so that the equation of function f(x) is: f(x) = [tex]ax^{2} +bx+c[/tex]
As it can be seen in thee figure, the graph of function f(x) cross points (0;8) ;(-2; 0) and (4;0)
=> f(0) = 8; f(-2) = 0; f(4) = 0
We have:
- f(x=0) = a x 0 + b x 0 + c = 8 => c = 8
- f (x=-2) = [tex]a(-2)^{2} -2b+c[/tex] = 4a -2b + 8 = 0
- f (x=4) = [tex]a(4)^{2} +4b +c[/tex] = 16a + 4b + 8 = 0
We have:
+) 4a -2b + 8 = 0 => 2 x (4a -2b + 8) = 8a - 4b + 16 = 0 (1)
+) 16a + 4b + 8 = 0 (2)
We take (2) minus (1)
=> (16a + 4b + 8) - (8a - 4b + 16) = 0
=> 8a - 8 = 0 => a = 1
Replace a = 1 into (1)
=> 8 x 1 - 4b + 16 = 0 => b = 6
So that: [tex]f(x) = x^{2} + 6x +8[/tex]
f (2) = 2^2 + 6 x 2 + 8 = 24
g (2) = 3 -2 + 2 = 3
=> f(2) is greater than g(2)
