$\begin{array}{l} \text{Gegeben: } \\ p_1: y=a_1x^{2}+b_1x+c_1 \qquad p_2: y=a_2x^{2}+b_2x+c_2\\ \text{Gesucht:Schnittpunkte zwischen 2 Parabeln} \\ \text{Parabel-Parabel}\\ \textbf{Gegeben:} \\ p_1: y=-1x^2-4x+4 \qquad p_2: y=-2x^2+2x-5 \\ \\ \textbf{Rechnung:} \\f\left(x\right)=-1x^2-4x+4\qquad g\left(x\right)=-2x^2+2x-5\\ \bullet \text{Schnittpunkte zwischen zwei Funktionen} \\ f\left(x\right)=g\left(x\right) \\-1x^2-4x+4=-2x^2+2x-5 \\ -1x^2-4x+4-(-2x^2+2x-5)=0\\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1x^{2}-6x+9 =0 \\ x_{1/2}=\displaystyle\frac{+6 \pm\sqrt{\left(-6\right)^{2}-4\cdot 1 \cdot 9}}{2\cdot1} \\ x_{1/2}=\displaystyle \frac{+6 \pm\sqrt{0}}{2} \\ x_{1/2}=\displaystyle \frac{6 \pm0}{2} \\ x_{1}=\displaystyle \frac{6 +0}{2} \qquad x_{2}=\displaystyle \frac{6 -0}{2} \\ x_{1}=3 \qquad x_{2}=3 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \\ x^{2}-6x+9 =0 \\ x_{1/2}=\displaystyle -\frac{-6}{2}\pm\sqrt{\left(\frac{\left(-6\right)}{2}\right)^2- 9} \\ x_{1/2}=\displaystyle 3\pm\sqrt{0} \\ x_{1/2}=\displaystyle 3\pm0 \\ x_{1}=3 \qquad x_{2}=3 \end{array}\\ \end{array}\\ \\ \text{Schnittpunkt }1\\ f(3)=-17\\ S(3/-17)\\ \end{array}$