x^2

+ 10x − 6y = −31

Looks more like algebra than trigonometry, but what the heck...

x^2+10x-6y = -31
6y = x^2+10x+31
6y = (x+5)^2 + 6
y = 1/6 (x+5)^2 + 1

That's a parabola with vertex at (-5,1) which does not cross the x-axis.