anonymous
  • anonymous
how do i find max/or min value of a function algebraically - the function is g(x)=3x^2-2x-1
Mathematics
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anonymous
  • anonymous
how do i find max/or min value of a function algebraically - the function is g(x)=3x^2-2x-1
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
its a parabola and the leading coefficient is positive , so it will have a min at its vertex
anonymous
  • anonymous
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
  • anonymous
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.....

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anonymous
  • anonymous
yes (1/3,-4/3) is the vertex
anonymous
  • anonymous
just evaluate g at x=1/3
anonymous
  • anonymous
you get y=-4/3
anonymous
  • anonymous
i.e. \[g(1/3)=3(1/3)^2-2(1/3)-1=-4/3\]
anonymous
  • anonymous
oh so basically just substituting the x value back into the equation! thanks so much!
anonymous
  • anonymous
yes

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