Plotting cubic curves

I wanted to understand how does one plot graphs for cubic functions.

for example ,

$y^2 = x^3 + 2x + 10$

Since this is a cubic function , i understand for every x value , y has a reflection along the x axis. Question being how does one compute the y when x is negative. Since you then end up with square root of a negative number. I am not sure what more i can try to solve this.

• You don't. Elliptic curves aren't plotted when the expression in $x$ is negative. – Parcly Taxel Feb 5 '17 at 0:09
• @parcly Taxel :Sorry , that begs the question how was this plotted : en.wikipedia.org/wiki/Mordell_curve – Bobo Feb 5 '17 at 0:11
• Just for the record, $x$ can be negative and $x^{3}+2x+10$ (for example) can still be positive. For example, $(-1,\sqrt{7})$ and $(-1,-\sqrt{7})$ are two points on the curve $y^{2}=x^{3}+2x+10.$ As for "how to plot the curve," plotting curves of the form $y^{2}=f(x)$ is something that is sometimes taught in high school. Typically it involves first plotting $y=f(x),$ seeing where the roots are, making things curvy according to certain rules and plotting something that is symmetric across the $x$-axis. – Will R Feb 5 '17 at 0:18