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