Jede quadratische Funktion lässt sich in der Scheitelpunktform darstellen:[br][math]f\left(x\right)=a\left(x-x_s\right)^2+y_s[/math] mit [math]S\left(x_s|y_s\right)[/math][br][br]Ausgehend von der Normalparabel [img width=61,height=19]data:image/png;base64,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[/img] haben die Parameter [img width=73,height=19]data:image/png;base64,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[/img] unterschiedliche Auswirkungen auf diese.[br][br]Aufgabe:[br][br]1. Verändern Sie die Schieberegler [img width=73,height=19]data:image/png;base64,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[/img] der Funktionsgleichung einzeln und nacheinander, um herauszufinden, welchen Einfluss der jeweilige Parameter auf den Graphen der Funktion [img width=12,height=19]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAcCAMAAABbGh8VAAAAAXNSR0IArs4c6QAAAEVQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOpDbZgAAZjoAZrbbZrb/kDoAkNv/tmYAtv//25A627Zm2////7Zm/9uQ//+2///bmxxaXwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZklEQVQoU72RwRKAIAhEwcrMTCvU///U8ibowekQN5ZhebMA/FJxQ5zv+hShBb/USjKsLaMTd4nn1SGkqKfApOyw1MpEEv2oezKc+92LugHtuLeg2QlQgI474UAMHaurycoo++m5D+knAvuWGxezAAAAAElFTkSuQmCC[/img]im Vergleich zur Normalparabel[img width=65,height=19]data:image/png;base64,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[/img]  hat. Zum Vergleich klicken Sie das Kontrollkästchen für die Normalparabel (rot) an.[br][br]Standardeinstellung für die Normalparabel: [br][br][img width=168,height=19]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPwAAAAcCAYAAABF79LlAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAfzSURBVHhe7Vy9cuJIEG5Rzv0ApEDgJfVWrfwAFDjhEgISLlkRWheQcXKhc8YFkB3a5EgISI5kYe8BIFhSzgEidX68AHNfjyR+DPbhNZIN0lQ5gfH8fNM93f11D2e1Wo2iFiEQIRAOBM7Csc1olxECEQKMQKTwkRxECIQIgUjhQ3TY0VYjBCKFj2QgQiBECEQKH6LDjrYaIXDyCm8UL0WzlKNuwabMvKNER+4/AhLz+h3p1siZTFVJq7YpPo7w9xN9o/hx0az/pjzG3colYrWaKU6etCueP4ir5C2x2KkFP6GOxvYQMIxLUVZyZKkNssWQEjSjQTlJuVyS1IYtokvXH1kxjI+LciyrWJ8aNAXuSYl7ysV9urjVDan0J2nh2cKUYdVLpFFaJRpB49OpBNHYH7CjUVcIDMpQdlKp0b6hjmlKj8po9YVm4XO9TlXREmP38wi3wyHwrZwlSwD3P28oRRSrmR0B3BfaF1wC+u/UX7QWOcWInZzCG0ZRNK/qdFG1pQtZPFeFxRofNd8RcKy7405d437tuDOa5ljJayQsy6LeoEVx31cSrgkc604K4w5Him6wfZP/zO+xnz7TArgrvW9/EOWU08vDmybixAxEauyJW7gO/013O+jBuqOlU0vr7q0neQFXC8HVZDqLFP7Qh/TtL/rCETpwTykKXPeajNe5JT6ouAkc3AmO/oaFZ+s4aNbpTrdk3MtN1fpUzffo7u6C2sOVm3boNb/VeEbxHHG+TiOOOX3aX/HyQZRyDqaIY5fkobSIV3B18YXWF/BIHBf4WNtsOnFk5gJmZr4ZPyVSaanwo3vs3zXxfmPP45dLusQXwG+c73JuuWKN+qJFxxpqrHBPAGHWdbbvrsIvcWeFT60U3nGFk6SPwKj2cShwh73PIKsskVu39r6CaUDgFTnIC5qPCviCVby6K+/9qpentqjQV8bXjWOzNCBP2Vng8lk4JT5wDEFib9/vETpNplRsGcKL718N8BMDODzOlCpDQZXmFSV1neqDm6V3YXbmyrCvOXKp5Q+u7EHiPvvHUfNnG3CfCrFYWnhmUnVpaYZLS8PucbGgCh0xsPYKiTTHceXlj3TmfMH83zbe/fe890x8jL2MycFyQtK7qjO51aC+fYPow1RgXXzZS1ixNztjJZ4BjwBcjcs09GFEVm9AtS0CAURXJUvzzmFv2/eKu1R4x71x3B7sndb37tzaKu3w0nwR0KAH5Zs+gxeDGfL/gklcF0iFpemWriB+/oUQQWP4ovnW4vvAsM/m4UNZZD3yLgY9tu59KPtxh1J74e/G91LhZ1+7Mr7UqpsxuuPS326xrntNEHXaRiCRIo5kLSr4xhe8JeweMfeWa9g9d5IczvCebLeDk1GAdbcPb92D3r9HzO0z79lSqXdZ8dlX6sqbYJt13Wdwr0+Q8cxL1hV439mUHForuBYk9ruIOW+nzxF6fqPBoellGmGuF06xkWvekaVVqeaTdX8b3B1ijmj1GxePCb01lj5Nj2tTBnWw16zvr4jf+TDfazzjt6Ctj++ETV1KayqNrC59nXG2dHcrXp6L0h2wX6VKUMjS+iHXM1DskxcwGzCkO4g5LzQsIEE/f4OMqed9IElALTeEXbfuh8Q8cJlPfKBPyO8w7kzMITqPmaZTSusQeioVkKAfQeSeLLyR7PLffHx0svE7722jFNSntJyXAkoj9daiMnEBCgvergKUVV83U8Jsc7K3dRkHeVntPVfimgoqX1SbF9pTBTlBYO+t3eFPOB89oCYuU/jyywv0qDHnDSZyVPjk4M4ksA6NZxu/qyDnbOXucBVURQoh543L0wpV06iBRpqOm7wBeylqt7I/nJ7bW3AO1FHWFZTBQaAxQ2sHkA7asOpuOvKWlwByKMN5diMvJIGE9YgWr69O08qa9bbv4VXhRk7CEoI4lmwzqGW/WPwDQS2HYVkyqprQkerSS03qtw2RTXBNd2mr3PaQ8+41lsef6Dmn5uImATl2//OIMXdxjxm/fl78krUU/WfG/WaRNYoO7hvltm4tfbZlU2OCtBzX5ZEqHvp42YSXZdm8JlRYIz2pUBcCeyzKzo9mSt0J3UpNcxtquZMgZVVVFenqKvW4/H5HddhegvRMJ8kCM6JL7MZQirFSaaDcF4KnWFzzAKzX48hshRoqzgKY4//EsWDuwcAhhLAbsuAlh4ImFwBYHhS2PBUv+4D99rF4xN1mnb/sd+SYS6X/Ho8t7OaiXLpRHuOeS3Bt/dprOacctUY15C1lc8tSZQ5ZpqzkhzKXfAytM8e6Uc6VyXgberTq8VrOW5aD+pOLHcdrqD/Yxq4zz+Bzd22PSoC9s7CrXJ2HS2qCKrDhcT044XRbfF2epEjtqDPwEfttObWJM8xqo73FhZwC5lLpO//GduG+/jO1J/d45iUXklPa+gDrM3za+rxkwAP27eCyHcJSctnvKT44CRJ7r2LUgqdVe+Y3EU4dcxbPUCs8u9dxeAI7rc8BlXffoWQqB2W4tsuTzJax5VZp+r5Dvtt+fmNfPP9blKhNw2sbJcxJ1NOzp5QFF7LppYYJ89Ar/HvTBs6iqhO48c4TGnGLX4ppoNQ5FJVgBz4MTgOOrCQpOg8MZWcOYcc7/LBhHmoLf2AZe/Vw7FJmEPuuUw/zdb7h1TOEY4BVMRkTpg2QzU+/8gwb5pHCh0MHQrXLTRLa/zcSxwRupPDHdFrRWiMEXonAf5B+ZNoJP3nxAAAAAElFTkSuQmCC[/img][br][br]2. Beschreiben Sie Ihre Beoachtungen für die jeweiligen Parameter. (Was macht der Graph?)[br][br][br]