Question 945443
Convert to vertex form by completing the square,
{{{y=3x^2+5x-7}}}
{{{y=3(x^2+(5/3)x)-7}}}
{{{y=3(x^2+(5/3)x+(5/6)^2)-7-3(5/6)^2}}}
{{{y=3(x+5/6)^2-7-75/36}}}
{{{y=3(x+5/6)^2-252/36-75/36}}}
{{{y=3(x+5/6)^2-327/36}}}
{{{y=3(x+5/6)^2-109/12}}}
The vertex is ({{{-5/6}}},{{{-109/12}}}).
For x-intercepts,
{{{0=3(x+5/6)^2-109/12}}}
{{{3(x+5/6)^2=109/12}}}
{{{(x+5/6)^2=109/36}}}
{{{x+5/6 = 0 +- sqrt(109)/6}}}
{{{x=-5/6 +- sqrt(109)/6}}}