Find the x- and y-intercepts.
Put x=0 to find the y-intercept: 23, so the parabola passes through (0,23).
To find the x-intercepts solve x2+10x+23=0:
(x+5)2=2, x=-5±√2, so the curve passes through (-5+√2,0) and (-5-√2,0) and of course through the vertex at (-5,-2).