Build a Digital Plotter

Python 2, 29 bytes

lambda n:1j**(n/2)*(1+n%2*1j)

Returns the coordinates as a complex number.

Mathematica, 24 bytes

Sign@{12-8#+#^2,4#-#^2}&

Pure function, using Sign and knowing where certain parabolas go.

C, 103 86 74 73 70 bytes

Thanks to @orlp for saving 12 15 bytes!

f(n){n="biM1*#?["[n]/7;printf("%c%d %d",n&8?32:45,n/4&1,n%2*~-(n&2));}

Try it online!