Question 493948
the function is 3x^2 - 4x - 2
set it equal to 0 to put it in standard form of:
ax^2 + bx + c = 0
this makes:
a = 3
b = -4
c = -2


since a is positive, the max/min point will be a min point.


the formula to find the max/min point is:


x = -b/2a


this becomes:


x = -(-4)/(2*3) = 4/6 = 2/3


when x = (2/3), y = 3*(2/3)^2 - 4*(2/3) - 2 which becomes:
3 * 4/9 - 8/3 - 2 which becomes:
12/9 - 8/3 - 2 which becomes:
12/9 - 24/9 - 18/9 which becomes:
(12 - 24 - 18) / 9 which becomes:
-30 / 9 which becomes -3.33333


you have x = 2/3 and y = -3.333333
that's the min point.


a graph of your equation looks like this:


{{{graph(600,600,-3,3,-5,1,3x^2 - 4x - 2,-3.33333,200(x-2/3))}}}


i placed a horizontal line at y = -3.333333 and a vertical line at x = 2/3 in order to show you where the min/max point is.


once again, this is a min point because a is positive.


if a was negative, the graph would be pointing up rather than down.