Question

Given g(x)=x^2-7x+1/4 show that the least possible value of g(x) is -12

Answer 1

`\displaystyle\\ g(x)=x^2-7x+(1)/(4) \\ \\ g(x)=x^2-7x+0.25\\ \\ \\ \\ x \text{ for } g_(min) = (-b)/(2a)=(-(-7))/(2* 1)= (7)/(2)=3.5 \\ \\ g_(min) = g(3.5) = (3.5)^2 -7* 3.5 + 0.25= 12.25 - 24.5 +0.25 = \boxed{-12}`