$\begin{array}{l} \text{Gegeben: } \\ p_1: y=a_1x^{2}+b_1x+c_1 \qquad p_2: y=a_2x^{2}+b_2x+c_2\\ \text{Gesucht:Schnittpunkte zwischen 2 Parabeln} \\ \text{Parabel-Parabel}\\ \textbf{Gegeben:} \\ p_1: y= \frac{1}{2}x^2-3x+2 \qquad p_2: y=-\frac{1}{2}x^2-1x+1 \\ \\ \textbf{Rechnung:} \\f\left(x\right)= \frac{1}{2}x^2-3x+2\qquad g\left(x\right)=-\frac{1}{2}x^2-1x+1\\ \bullet \text{Schnittpunkte zwischen zwei Funktionen} \\ f\left(x\right)=g\left(x\right) \\ \frac{1}{2}x^2-3x+2=-\frac{1}{2}x^2-1x+1 \\ \frac{1}{2}x^2-3x+2-(-\frac{1}{2}x^2-1x+1)=0\\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1x^{2}-2x+1 =0 \\ x_{1/2}=\displaystyle\frac{+2 \pm\sqrt{\left(-2\right)^{2}-4\cdot 1 \cdot 1}}{2\cdot1} \\ x_{1/2}=\displaystyle \frac{+2 \pm\sqrt{0}}{2} \\ x_{1/2}=\displaystyle \frac{2 \pm0}{2} \\ x_{1}=\displaystyle \frac{2 +0}{2} \qquad x_{2}=\displaystyle \frac{2 -0}{2} \\ x_{1}=1 \qquad x_{2}=1 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \\ x^{2}-2x+1 =0 \\ x_{1/2}=\displaystyle -\frac{-2}{2}\pm\sqrt{\left(\frac{\left(-2\right)}{2}\right)^2- 1} \\ x_{1/2}=\displaystyle 1\pm\sqrt{0} \\ x_{1/2}=\displaystyle 1\pm0 \\ x_{1}=1 \qquad x_{2}=1 \end{array}\\ \end{array}\\ \\ \text{Schnittpunkt }1\\ f(1)=-\frac{1}{2}\\ S(1/-\frac{1}{2})\\ \end{array}$