## anonymous 5 years ago how do i find max/or min value of a function algebraically - the function is g(x)=3x^2-2x-1

1. anonymous

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

2. 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 $(x,y)=(\frac{-b}{2a},g(\frac{-b}{2a}))$

3. 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.....

4. anonymous

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

5. anonymous

just evaluate g at x=1/3

6. anonymous

you get y=-4/3

7. anonymous

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

8. anonymous

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

9. anonymous

yes