Question

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

Answer 1

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

Answer 2

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 \[(x,y)=(\frac{-b}{2a},g(\frac{-b}{2a}))\]

Answer 3

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.....

Answer 4

yes

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

Answer 5

just evaluate g at x=1/3

Answer 6

you get y=-4/3

Answer 7

i.e. \[g(1/3)=3(1/3)^2-2(1/3)-1=-4/3\]

Answer 8

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

Answer 9

yes