Hasta ahora, se ha representado una gráfica mediante una sola ecuación con dos variables.[br]En esta sección se estudiarán situaciones en las que se emplean tres variables para representar una curva en el plano.[br][img]data:image/png;base64,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[/img][br]Considérese la trayectoria que recorre un objeto lanzado al aire con un ángulo de 45°.[br]Si la velocidad inicial del objeto es 48 pies por segundo, el objeto recorre la trayectoria[br]parabólica dada por:[br][img]data:image/png;base64,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[/img][br]como se muestra en la figura. Sin embargo, esta ecuación no proporciona toda la[br]información. Si bien dice dónde se encuentra el objeto, no dice cuándo se encuentra en un[br]punto dado (x, y). Para determinar este instante, se introduce una tercera variable t, conocida como parámetro. Expresando x y y como funciones de t, se obtienen las ecuaciones[br]paramétricas[br][img]data:image/png;base64,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[/img][b]Ec. para x[br][img]data:image/png;base64,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[/img]Ec. para y[br][/b]A partir de este conjunto de ecuaciones, se puede determinar que en el instante el[br]objeto se encuentra en el punto (0, 0).[br][br]