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CLEI I
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Propósito
<p><b></b>Establecer representaciones de la función cuadrática a partir de situaciones que modelen su comportamiento, hallando las raíces y ubicándolas en la gráfica de una función cuadrática.</p> <ul><li>Reconocer situaciones de su entorno que modelen movimientos parabólicos.</li> <li>Establecer características de la función cuadráticas a partir de diferentes tipos de representaciones: gráfico, tabular, entre otros.</li> <li>Reconocer las raíces de una función cuadrática a partir de diferentes representaciones ya sean simbólicas o de procedimientos algebraicos.</li></ul>
Motivación
<p>¿Para qué las ecuaciones funciones cuadráticas?</p><p>En nuestras vidas realizamos actividades como el lanzamiento de una bola de basquetbol, cuando observamos una antena parabólica, las fuentes de agua, entre otros, los cuales nos permiten dar respuesta a muchos interrogantes de nuestro contexto.</p><p>Espero te sirva este video para aclarar dudas:</p><p><u><a href="https://contenidosparaaprender.colombiaaprende.edu.co/G_9/M/M_G09_U04_L02/M/M_G09_U04_L02/M_G09_U04_L02_03_01.html">https://contenidosparaaprender.colombiaaprende.edu.co/G_9/M/M_G09_U04_L02/M/M_G09_U04_L02/M_G09_U04_L02_03_01.html</a></u></p><p><b></b></p>
Explicación
<p>Es importante recordar:</p><ul><li>Números Reales, operaciones básicas y propiedades.</li><li>Plano cartesiano.</li><li>Representación gráfica en el Plano Cartesiano de una función.</li> <li>Método Gráfico.</li> <li>Propiedades de la Potenciación.</li></ul> <p><i></i></p><p><i></i></p><p>Ya recordamos algunos conceptos básicos. Observemos los siguientes vídeos, espero con los vídeos que ilustre les sirva de apoyo para entender el tema. Video Para calcular las raíces:</p><p>Video Para calcular las raíces:</p><p><a name="_Hlk80626507"></a><a href="https://es.khanacademy.org/math/4-secundaria-pe/x2e479127ce193f05:algebra-ecuacion-y-funcion-cuadratica/x2e479127ce193f05:formas-y-caracteristicas-de-la-funcion-cuadratica/v/rewriting-a-quadratic-function-to-find-roots-and-vertex">https://es.khanacademy.org/math/4-secundaria-pe/x2e479127ce193f05:algebra-ecuacion-y-funcion-cuadratica/x2e479127ce193f05:formas-y-caracteristicas-de-la-funcion-cuadratica/v/rewriting-a-quadratic-function-to-find-roots-and-vertex</a><b></b></p>
Ejercicios
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAk0AAAAlCAYAAABfwt1GAAAHu0lEQVR4Ae2dwW3cOhRFpwd34EU6yCbb9GDvsnMDQQowsjbcQLxPAYG9twtIASnALiAF6OMOcAfPLyRFaSRNfnwIGByRj4+XZwLwglI0u4ECAQhAAAIQgAAEIDBKYDcaQQAEIAABCEAAAhCAwIBp4h8BBCAAAQhAAAIQ6CCAaeqARAgEIAABCEAAAhDY/f79e/j48eOw2+2Kf+fn58Pz8/Oe1M+fP4d3794Nqk9Z/hYdp2TA3BCAAAQgAAEIbEvgYJpubm62nfmI2TBNR8BjKAQgAAEIQAACswhgmmZhYxAEIAABCEAAAm+NwCTTlE948q29eCtPIB1/d3c3nJ2dHW7/6VRLfbHtx48fe/Ye8/Xr10O8bh9qLhfHqHbJWj59+uSufe3+/9OJ2qsFcAEBCEAAAhCAwEkJzDZNNiHRnMiQRINjYxTbFKPnp3KbDZfH+Lo0TzZNOSZfn5Qwk0MAAhCAAAQg8E8QOJim2oPg8WQmmhWdDNnYmIQeGFdbPDXSaZKvFWdTlNv8gPlYv3M4XtclLaU266SGAAQgAAEIQAACUwkcTFM0R7Uk0TT5xKhktpwrxjvnWFupv2TGsmmKJ1eaq5THGqghAAEIQAACEIDAVAJHmaZsVPLkJeMy1lbqxzRlslxDAAIQgAAEILA1gdmmSbe/dOtNJqdWSgZorE39pVt679+/r74vqqSF23O1b4V2CEAAAhCAAATmEJhtmvywdTxtyuZlzCBZcIyzafLzUp4nPnAe45Ujx+Rrz0MNAQhAAAIQgAAE5hI4mKbSs0lqi6dJNbPisTFWgnJ8T5vHxFcORMNUy2GjZC15jPv9vNVcYIyDAAQgAAEIQOBtEpj023M2NKrXKlvMsZZ28kIAAhCAAAQg8O8SmGya4rNFa2DBNK1BlZwQgAAEIAABCBxLoNs06XaXbn3l217HCsjjMU2ZCNcQgAAEIAABCPwNBLpN098gFg0QgAAEIAABCEDgVAS6TZMepH56ehoeHh5e/Q7cqYQzLwQgAAEIQAACENiSQJdp0i2zi4uL4devX8Pj4+Ow9nNNWwJgLghAAAIQgAAEINBDoMs0xUR6O7dMk4wUBQIQgAAEIAABCLwVApNNk8zS58+fV+Oj/Hrfk9+3pDq+QHO1icNLMj137Z1Ofij+WG1+d5ReCrpk8c/OlNYx1fSuoVHfcfztQK19qq4leZELAhCAAAQg0ENgkmnSxnZ5eXn4OZOeCabGyEBsZZKyNpkh/+9AG49snNQf23Q9V6/yeL6sZe61TY41+TpqnsJ4aY3Wk1+EqvVO0TWXD+MgAAEIQAACcwl0myZtdl++fJlsmEqnCi2xS2/SrbliX0mntNh8KLYUU2qLeWufjzlZac0p45ENidr8szTSY+Oi9lY5RmMtr5jqlCmfNE3RVctNOwQgAAEIQGBNAt2m6fr6+vAckx4I119PaW3wpfH5JCfHaNONpqB2IpTHzbnOpqnnJETrzbcXfZss6s65p6yrxTQbJK27FN+zlqxRuabozMylQ8/D3d/fF02T4nt05bxcQwACEIAABLYgsDdNMkDazOKmrueWfG0j8OHDh0F/bu8RWNqwa+NsgDSHjUY8IfE4GSvf1oqf3b9EbS3axF1kGDSf2lr6HF+rfdKjfLHEtcTPMUafW0ylLX8/1hvX0sqhOWoa1Re1xc9ZZ7x2Pmlozd3qi/n4DAEIQAACENiawP4He29vb4eXl5f9rSht5N++fRu+f/8+W4s2Pm3cNhaxLpkgT+Rx0UyoLb/iwBvr3d3dH33ONbf25i7N8dac8skgqF21i0xAjnNfrS4ZMsW21mU2kaU/R6bObY1xPdE0OS62Rb2t/pbOmCN+tuGM61SeXFrz5liuIQABCEAAAlsSeHV7ThubzI5M01LFG2xpg+yZo7aJSqtMQ23T78k9FqPc0ZDIiGSDVNPXyt0a07OuMabOLz76PmUu8zNENlOar1Sco8a3R6fzSm80vi39Y7qckxoCEIAABCCwNYFXpimbhCXEtDbInvy1zbt06lPK583dpzI1k1Aam+fWWJ/gOD7HaL21Uza1qz+PcS7VPeuayrQUP2ZOWhprOmusc7u/i5LpHdMVWfEZAhCAAAQgsCWBg2nSZnV1dfXHicSxYkobdi1nybRp89YphfK4OE5tOgmqnYY4vqd2Ts3nko1DLSbr8/hanfM6zvnH1tViWuqTaZl6QlbTKK29Or2uXJc0OqY1r2OoIQABCEAAAqcgsDdNMkx6nYAeCNfmqk1WG9sxzzXNWYxPGbQpu+hz3PDzpuoNXO3HlJ65HSM+LiVD4r5WrROlmGepdVmjT8T0PeqEKzKVrpZxse6sUe1L6GzN3eqzLmoIQAACEIDAKQjstDHGkxJt5LptsuZbv1sL9absWzjRMGmc9Ma2bBJaucf6nKs2t8b3xIzNo/5sBpdcV2aYDZPm7zF7WaPGLaGzZYx6dPXwJQYCEIAABCCwNIHD7bmlE5OvTUDGJprVdvSyvTZ+JTMVZ9paY6+uqJHPEIAABCAAga0IYJq2Il2YR6cqOrnZupROkGoattQ4RVdNL+0QgAAEIACBtQhgmtYi25H3FCcrU0+PttI4VVcHXkIgAAEIQAACixLANC2Kk2QQgAAEIAABCPyrBP4DJSwx/J8WEkAAAAAASUVORK5CYII=" alt=""><img 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dg4T5nHMdfIHfFiv8gJHMM5diqj7SoxEE3ytwrvsmsXq9k3ihCpjrN0PMZxDU/td5oQI7JDtGgeT9lpko2+LafHjNzLDv/nK+2jQPHuoibmUhJNYGf3DJ+132ly/5qnq4omzcv33X28F07cX/tHlRXR1OW/+BtIC/nbI7GY/9bfK/ph/w1E9W0x3TXH9Ht3HGvv+WBCXMXfYCrFj32GfqfJRdNYfvSViGGnTHNH33zTeETRJH9b8z7RHLf/3djBbwc+f/RK/w6bx5NvzTHqIr95vjsZWBBNuxNiomLx1A3YBV8ykwzsNAPdQj//yYCdxpPxk4FkIBnYTgZSNG0nu2vynaJpTUSmm7UxgFiSkNc/vcPDC8hrC5KOkoFkIBnYZQykaNplA1KCk6KpxErW7SQDLpq6l6jnv6Gzk7gydjKQDCQD28lAiqbtZDd9JwPJQDKQDCQDycAbhoEUTW+YocxEkoFkIBlIBpKBZGA7GUjRtJ3spu9kIBlIBpKBZCAZeMMwsEU0ffCDH2z27dvXHDx4cEuS+kr+VVdd1dx3331b2na6YqewPf74483ll19e5AwuxdnQzxmsm7t1caE5oLlQmw+aB2pTnjvxWVeeO4F9L8YU31dfffXS17/myW68Z1zsGCinK664ojl69OjFutpiv52+twSbWKF7nfL9xje+MfjS//3339+O9yZ/MUDXyjXXXDPK1RD1t956a7N///72HnvLLbds4Vw8X3bZZc0HPvCB5rXXXhtytW1t5Pn1r399C75tC7rDjhdEky6KN73pTc11113XiiMR4h+dp2hyRrpjxIXEkzjURzc9BMelXjDWMU74KIln5adfg3/HO95RFNcdK9v/XzBean63P7PdGUF8LyuaVrHZndlvRbWdwmY7fW/NZFrNFNHEeI8Jq2kR924v8XAxogn7klgSK7r/vutd72pq7ZeKOXBurGjSAilRdPjw4Xb3JC5GIihF09bpCC8SSRISZ8+ebUvOa//ft62e1lMDnjh+y3hfh49l4q3Sdy9gXCWv3WojvlM0zUdnO4XNdvqeZ7DcUYqm6XzpWlmHaNrt4pM8N1I0sXOgRy1+7NNkbJFS+1ve8pbm5ptvbndZ/LEUuzHsvsQdDF2QPOaiT1z0dU6bSvcBNsWWn5Kt7wQpryFMQ7k4Jxw7Nu3WCV+MR99YjuEQj4cOHWoFK/nH/NwnXMQ+PC4c8xHHwsdRcTzX0jjEOYAIjzko7xgLzKUcYl08h4Opeaq/4mu87rzzzoX553Nril9hiXmrTp9l8BArzgn58M/QGMDpMnzL9xgXyqckmiJWuJM/Pc5hvukPivOz/2Hphz70ob5e7Voc+CjOW9/61vY+oscTmn/+6+X0o1Q8HmPIl7jSoyHwRt/KwevkZwgPcfxxia7tT37yk/3juSHM8u34Ymz5H/JNfI25+4m7DJHvyCt+hko98qnFwD95M67goJ16H++Yo/pgxzjdcccd7fzCXjzFR3zOk/uQf8W/8sorm+hHcfQIVW0130N5u2/sVQ4JBeUURVOcBzV78iCW5v+pU6f6YeOxHO3wqA6K+7a3va2dmxpH2WreTOXFMZHDUF2pz4c//OGFOeT27JDpGt2pR4o9kSse9I/nRKwv8roR+TkDwiCU4olAteti8d2V6EuTQr795qpzYeCjY00K6uI5sVhMOL/nnnva+NTjT+eOawwT/twGX7VSMZjIKsmv1l/1U3H4WESb6B/scKd2YXNOVvEhP1PHwXljvGMO4kjzRXj1ESbOSznEuni+Sp5gG5prU/yCxfOeYqc+8RPHBt+q12dsDMhpGb7lV3aIHBZ2xdLNV+fCEUUTWHmvBx9gLdlo8dBcZEGMPrARl4isyBHnNVvV44dcZFOqi3i0MMd3ldRHcxPxBi/iWLnjN2Jeh2/hJh65EA8e4Z32kg2c1UqP4aIzxiBn+SEuCze4hIPxVb/IqduJU80r9xv7j/lQLPmUOJCfxx57rE0TkaWxQ3ioTvE4RzCBWTlI8OhdIfdLuxwjXFwQtAFn/8EHNrV5AE631XG0pz3GpR/vNXGuefjqq6+2Zk888cQCL8ppCi/48hxjXTyXYNJ8QRAxjsrT5wP57MWyF01K1G/4IkMTjZufkqNOF1fpQ3vJxutkKx8skH5c8svOV8mHLhBdLMSWL/XDt/zRhn08J6bjqPWhb6kUDuHRAuxclvqqrhZjDAdx1K/0wS/tOtcuiOz4LOtDdsuMA1zLjlhT64Q75iA/sa50vmyeJWyKJayM4RT+wOI5TrFTLP+U/Hj7lDEo5TRUxzxRH4kFz0Gx4eLZZ59dEE3CqsUn9pc/XX9aDOlDDJ1rFwmRJf/E1QKjDzbRb9to/xnrRzt+3Td1U/BEfEDQQshCTyzEA7HGcp3iW2P+zne+s+XZFx5xirjTscYCUQfGqWUthhZpYoDVc5R/RIiPN2IBHoQt2sm36jUXYjux8CN+JWRqPiSAZCPR5H2G6uRbolzcuo0wk7cWe7hFZE3hFLyKoWPt/sQ5L6zkF326PWOuMSq9xySs8iWs2Hk+iKapdYgkfHHOWGocqPM+Gn/l6QKJ2PSPee7F81Y0aWLp4o83KQmpkvjgBhgTFoHq7+06Rth4f2KqHTuPVetbq8eH+wNHxBDP8VnChA/6DJXiT4KJf2O2q+LwXEt4xtoVdwxjyYfz43G9fqqd2+DL60p+Yl08xw/llDw9JnYqa2NDW+RvDEvNzmPquIaHfrV2r/fjIbvYT+daIJW7f+BCj1n9+qbeFwPZ4YcFQwti9Il/1fM4SP31EZey4Zy+sfQ4sa3mZ8x3CY/qhCcKEtUjKMb8Cs+qvmt5ej3xNT4RZ4mbWOe+WKTVx+v92PsgMDQPwOFiwNs9Lv54nOY28uOPt8Z8yFb+ohAZqyu1kze+wCJupwonbDwnclcu+tab7iE1MVGyB2u08XqNvfOmmCXhMqUODB4v1sVzclQ5JU/vv1eOW9EUF3sWBEpd7PqIIL9pxiRL7bLFT6nEN39Bex/aNCkkvDgnrsfzY7VL8Okfx+wa6HwKpuivdTTwHzA6fnElP7XPqjjGsJXafYyFi/eMIqdgLfkgx2jjff0YXyW7sbqSn1gXzxVv2TyFQ+80qfSPcnSxP+a3hGWdeMBW4k1tHr/UZ0qd+gxxURJNCB6f9xxrwRCuKJoilyyI6k8uU0XTtddeu/AXPDzV/ICHWOrHowrh1rUR8fhOivvXHBkTTevwrXFRHMdcyo/dIvhXGW0cvx97DBdEzpf6lPj2eu+PH/E5NE+miqYhH8pTOBA6xB6rK7XDrYsPdnkcg4sJ57JkX5oHEav7EI8eX21gjXG9706LJuWJIEQrKM+I2XPda8f7ECsIDE9Ag6HEaeM8LprYlNrj4kPfsVIxWbQ0WUqiyetjbMUVdvVh8Ig5BVP0h22tFF5uuggSnWuBqH1WxTGGLbY7T2Ap1dGmMvpQXc3G66fauQ1xva7kJ9bFc7cv+aTOS9kMCQW1T/EbsSjGFDvHUrPxPiWf0a7UZ0qd+gxxURJNui7jTpPjFS8umhQjCoBYh83Ygh/tPK6OS35iXclHrNN1uspOU/TDOHn+U3yX/JR8xfz98WFsi+ceA8ERY9T6IDKX3WkCg48JsVXnosFjYBdL4YtCZKyu1E7e0ZfHE7caRz2KKn0cfylGqc79uD2cYBMFiNfvpGhyHGAu7Wh5nnvxeN/Ywq1FH/GigYwCxJMutZfq3KZ27HYIuyhAHLv3l0/OP/KRj7SYdc6HNtnXPlP6YCs//HWHT/6ahjv6ejklRqlPqW7IrzBp3GTHB8zgpZ6yFGOVcZA/XUxR9I7VEd/HPNrQhxxWyROfHkeYJYLZnZziN2KRjyl28E2Jn4iH9iljQE7wItspdeqjhSDGhovaO00eB5yUysdFE5z4IyTV6S94RBI2nOMrlvSLeOnn7dzEyRHfih0FUcQTbfCvv6rFVxQLtK/Lt8Z87J0mYnpJ/uTqbfG4FsPFCjz4uzHyIx50rej9II8J56U6j19qV52Lpnju9hwLXxQ6Y3VT3mnCv5djeLydeeCP9sSrdmSiACKG28OjxmjqO00ac+xKwmVKHRh8vKMdfZSH8tSYLZMn+e6lch83RA1I6aNJpwVPNyYRtKxokk/ZRvGguNSJbI7BEOt0LmGiUh+wyI+f0646tcmGPm3H2X/GMOHf/bk9x/SLccSnbiSqZ/HFxstVcBCzhi22M4b0p13YFL/0oQ829NG57KinHxxzTrvsYvwpdfAHd5yXYhMrxgHLUJ7Y+PyLOdKHOCW/1NGnlCN9hvDILs4JcofjiA+/tEe8JSylOtlJBIgLdo8UC0GjOC6AHCv9Vec7HNgwz4jBQk67c0IdfeSz9oEr4osrCQxxwYLIgk6bYuF7CI8vFi6QhAVe4KqEeV2+PR64iac8tTgKDwIOrkp1tJVKclIM+YwxyIec5UOLP/PDbZw79Yv8qY7dGvnQvCKu2hTbRdOYD42/8C0rmoS5lINi8+05tYtb31Uq1QkjH8cfcdGmeRh5KtkLIx/FdbGFr/jtOecyCh35mlKn60UiTdePvonHucYbsUd8nZNnbFOen/70p3sRRy57tdynC0AXy9BHF6bEkkhZRTTJt25uIo9/tZ0P2oVL8fwjnLSr5EasPhq8iI3+tfyGMJX8ORaOxY2wxHzULvzKI2LFlnJZHGPYSu0eA26FnWOwUJZ80AavjMXYOMCDj8OUOjAQh98dwg/tnAvfsnmCg9/3Ipb7nOK3hGWKHZzG0vMQJo2Vf4QPrCp9DMjJc5hSpz5aHCIXcaF2v8IUsepa8J0kLY7CiHjx/pp/WvCYizoWlyyinnPtWP50I4cP+WKhwRdt/v4M/rSgYw8eF361fvxe0RDmdfgmvngHp/KJC25sJxfZIxidG/x6iYCAL4/B/CBv+vgCLV/iTjgZb/w7F7JlnjBG7kd1UTTJT8kHOxvCt4pokt+hvGnnXR1hF7cuosiRMuJ33NgiGkt+oj1+S1h8jEp2UwSS/Jb64Y+xvv3229trMwojzpUnPJXyRHhpHvKzBJ7bXjjuf3JgL4BNjMnAuhkoiYl1x9gr/lgUoyjaK/gT5zADGt8bbrihF5TDvbM1GUgGSgykaCqxknUbw0CKpvlQp2iac/FGPJIY1q4cu3BvxBwzp2RguxlI0bTdDKf/Xc1Aiqb58KRomnPxRjzSLpMeJeYnGUgGVmcgRdPq3KVlMpAMJAPJQDKQDGwQAymaNmiwM9VkIBlIBpKBZCAZWJ2BFE2rc5eWyUAykAwkA8lAMrBBDKRo2qDBzlSTgWQgGUgGkoFkYHUGUjStzl1aJgPJQDKQDCQDycAGMZCiaYMGO1NNBpKBZCAZSAaSgdUZSNG0OndpmQwkA8lAMpAMJAMbxECKpg0a7Ew1GUgGkoFkIBlIBlZnIEXT6tylZTKQDCQDyUAykAxsEAMpmjZosDPVZCAZSAaSgWQgGVidgRRNq3OXlslAMpAMJAPJQDKwQQykaNqgwc5Uk4FkIBlIBpKBZGB1BlI0rc5dWiYDyUAykAwkA8nABjGQommDBjtTTQaSgWQgGUgGkoHVGUjRtDp3aZkMJAPJQDKQDCQDG8RAiqYNGuxMNRlIBpKBZCAZSAZWZyBF0+rcpWUykAwkA8lAMpAMbBADKZo2aLAz1WQgGUgGkoFkIBlYnYEUTatzl5bJQDKQDCQDyUAysEEM/D8mF3IAiwE/LAAAAABJRU5ErkJggg==" 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" alt=""></p>
Evidencia
Evaluación
<p>En las clases virtuales nos pondremos de acuerdo.</p>
Bibliografía
<p>Ministerio de Educación Nacional, Editores SM, S.A.2.017 vamos a aprender Matemáticas 9 Guía del Docente. Bogotá<b>, </b>D.C., Colombia.</p><p>Gladys Vergara Saavedra. Educar Editores S.A. 2.009 Bogotá, D.C., Colombia. </p><p>Misión Matemáticas 9. Libro del Docente y libro del estudiante.</p><p><u><a href="https://es.khanacademy.org/math/4-secundaria-pe/x2e479127ce193f05:algebra-ecuacion-y-funcion-cuadratica/x2e479127ce193f05:formas-y-caracteristicas-de-la-funcion-cuadratica/v/rewriting-a-quadratic-function-to-find-roots-and-vertex">https://es.khanacademy.org/math/4-secundaria-pe/x2e479127ce193f05:algebra-ecuacion-y-funcion-cuadratica/x2e479127ce193f05:formas-y-caracteristicas-de-la-funcion-cuadratica/v/rewriting-a-quadratic-function-to-find-roots-and-vertex</a></u><b></b></p>
Foro
<p>Les aclararé las dudas e inquietudes en las Clases Virtuales.</p>
calificable?
Activo
Actualizar