4. Which of the following functions is equivalent to g(x)=(2)/(5)(x-5)^2+8 A g(x)=(2)/(5)x^2+6 B g(x)=(2)/(5)x^2-4x+18 C g(x)=x^2-10x+33 D g(x)=(2)/(5)x^2-10x+33

To determine which function is equivalent to \( g(x) = \frac{2}{5}(x-5)^2 + 8 \), we need to expand and simplify the given function.<br /><br />First, let's expand \( (x-5)^2 \):<br />\[<br />(x-5)^2 = x^2 - 10x + 25<br />\]<br /><br />Next, we multiply this result by \(\frac{2}{5}\):<br />\[<br />\frac{2}{5}(x^2 - 10x + 25) = \frac{2}{5}x^2 - \frac{20}{5}x + \frac{50}{5} = \frac{2}{5}x^2 - 4x + 10<br />\]<br /><br />Finally, we add 8 to this expression:<br />\[<br />\frac{2}{5}x^2 - 4x + 10 + 8 = \frac{2}{5}x^2 - 4x + 18<br />\]<br /><br />Thus, the function \( g(x) \) simplifies to:<br />\[<br />g(x) = \frac{2}{5}x^2 - 4x + 18<br />\]<br /><br />Therefore, the correct answer is:<br />\[<br />\boxed{B}<br />\]