Find the zeros of y=3x^2+x-2, then use the zeros to find the vertex of the graph of the parabola.

First off, let's find the zeros, keeping in mind that, the vertex of the parabola, will be half-way between the zeros.



now, the zeros are there, now, what's half-way? or the midpoint of that interval?  well, from -1 to 0, is say 3/3, from 0 to 2/3 is 2/3, we add both to get 3/3 + 2/3 the interval is 5/3.

now, what's half of 5/3?    

now, 5/3 is the same as 10/6, so if we move from say the -1 spot over 5/6 towards the 0, we'll end up at -1/6.

therefore half of 5/3 is 5/6, and if we move from either "zero" to the middle by 5/6 units, we'll end up at -1/6, check the picture below.

therefore, the vertex is right there, above -1/6, when x = -1/6, what is that anyway?