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Math·Advanced Math·Nonlinear functions

hard

$g(x)=x^2+\frac{27}{2}x$

Which expression represents the minimum value of the given function?

A

$-{\left(\frac{27}{2}\right)}^2$

B

$-{\left(\frac{27}{4}\right)}^2$

C

${\left(\frac{27}{4}\right)}^2$

D

${\left(\frac{27}{2}\right)}^2$