ascherbaum, 
That's what #ChatGPT gave me when I asked for a #gnuplot script for a Parabola, and plot a vertical and horizontal line crossing the zero point.
I don't see a vertical line, and neither does it cross or touch the zero point.
The generated plot command:
plot f(x) with lines title "y = x^2 - 4x - 5", \
2 with lines title "Vertical Line" lc rgb "red" lw 2, \
-9 with lines title "Horizontal Line" lc rgb "blue" lw 2