Main function: [math]f\left(x\right)=ax^2+bx+c[/math][br][br]Reciprocal function: [math]\frac{1}{f\left(x\right)}=\frac{1}{ax^2+bx+c}[/math][br][br]Roots of the main function: [math]R_1,R_2=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/math][br][br]Asymptotes of the reciprocal function:[br][br]Horizontal: [math]y=0[/math][br][br]Vertical: [math]x=R_1[/math], [math]x=R_2[/math][br][br]Intercepts: [math]\left(I_1,-1\right),\left(I_2,1\right),\left(I_3,1\right),\left(I_4,-1,\right)[/math], where [br][br][math]I_1=\frac{-b+\sqrt{b^2-4a\left(c+1\right)}}{2a}[/math][br][br][math]I_2=\frac{-b-\sqrt{b^2-4a\left(c-1\right)}}{2a}[/math][br][br][math]I_3=\frac{-b+\sqrt{b^2-4a\left(c-1\right)}}{2a}[/math][br][br][math]I_4=\frac{-b-\sqrt{b^2-4a\left(c+1\right)}}{2a}[/math][br][br]For the general intercept, [math]\left(I_{1-4},\pm1\right)[/math], the sign on the 1 is indicated in the [br]diagram below.