Question 834682
Complete the square and get the equation in vertex form, {{{y=a(x-h)^2+k}}} where (h,k) is the vertex.
{{{3x^2-5x+7=3(x^2-(5/3)x+25/36)+7-3(25/36)}}}
{{{3x^2-5x+7=3(x-5/6)^2+252/36-75/36}}}
{{{3x^2-5x+7=3(x-5/6)^2+177/36}}}
{{{3x^2-5x+7=3(x-5/6)^2+59/12}}}
(5/6,59/12)
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{{{ drawing(300,300,-2,6,-1,7,grid(1),circle(5/6,59/12,0.1),
graph( 300, 300, -2, 6, -1, 7,3x^2-5x+7) )}}}