Question 947491
{{{3x^2+2x-5}}}

{{{3(x^2+(2/3)x)-5}}}....complete square

{{{3(x^2+(2/3)x+1/9)-3*1/9-5}}}  

{{{3(x+1/3)^2-1/3-15/3}}}

{{{3(x+1/3)^2-16/3}}}


since
{{{h=-1/3}}}
{{{k=-16/3}}}

the vertex is at ({{{-1/3}}},{{{-16/3}}})


the minimum y-value located on the graph is {{{y=-16/3}}}


{{{drawing( 600, 600, -10, 10, -10, 10, circle(-1/3,-16/3,.13),locate(-1/3,-16/3,V(-1/3,-16/3)), graph( 600, 600, -10, 10, -10, 10, 3(x+1/3)^2-16/3)) }}}