Question

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Answer 1

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) = $ax^{2} +bx+c$

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) = $a(-2)^{2} -2b+c$ = 4a -2b + 8 = 0

• f (x=4) = $a(4)^{2} +4b +c$ = 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:  $f(x) = x^{2} + 6x +8$

f (2) = 2^2 + 6 x 2 + 8 = 24

g (2) = 3 -2 + 2 = 3

=> f(2) is greater than g(2)