how do i find max/or min value of a function algebraically - the function is g(x)=3x^2-2x-1

Question

anonymous · Answer

its a parabola and the leading coefficient is positive , so it will have a min at its vertex

anonymous · Answer

since g is of the form $$g(x)=ax^2+bx+c$$
the formula for the ordered pair that is the vertex is given by $$(x,y)=(\frac{-b}{2a},g(\frac{-b}{2a}))$$

anonymous · Answer

the x value matches the calc min x value! now i just have to do my y- so what is the value of g to calcuate that? the value im supposed to get is -1.3333333.....

anonymous · Answer

yes

(1/3,-4/3) is the vertex

anonymous · Answer

just evaluate g at x=1/3

anonymous · Answer

you get y=-4/3

anonymous · Answer

i.e. $$g(1/3)=3(1/3)^2-2(1/3)-1=-4/3$$

anonymous · Answer

oh so basically just substituting the x value back into the equation!
thanks so much!

anonymous · Answer

yes