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Консультация № 70766
13.01.2007, 18:07
0.00 руб.
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2
2
помогите пожалуйста!!!
задание:
Составить уравнение параболы, симметричной относительно прямой
x= -1 и проходящей черех точки М1(1;7) и М2(2;17).
надо очень срочно!!!!!!!!!!!!
заранее спасибо!!!
задание:
Составить уравнение параболы, симметричной относительно прямой
x= -1 и проходящей черех точки М1(1;7) и М2(2;17).
надо очень срочно!!!!!!!!!!!!
заранее спасибо!!!
Обсуждение
Неизвестный
13.01.2007, 18:26
общий
это ответ
Здравствуйте, Toljn!
Если парабола симметрична относительно x=-1, её вершина имеет абсциссу -1.
Пусть её уравнение y=ax^2+bx+c
Абсцисса вершины = -b/2a=-1; b=2a.
Парабола проходит через указанные точки => их координаты удовлетворяют уравнению.
7=a+b+c
17=4a+2b+c
Решая, a=2, b=4, c=1.
Так что искомая парабола y=2xx+4x+1.
Если парабола симметрична относительно x=-1, её вершина имеет абсциссу -1.
Пусть её уравнение y=ax^2+bx+c
Абсцисса вершины = -b/2a=-1; b=2a.
Парабола проходит через указанные точки => их координаты удовлетворяют уравнению.
7=a+b+c
17=4a+2b+c
Решая, a=2, b=4, c=1.
Так что искомая парабола y=2xx+4x+1.
Неизвестный
13.01.2007, 18:30
общий
это ответ
Здравствуйте, Toljn!
из первого условия следует, что вершина лежит на прямой х=-1
то есть -1=-в/2а, в=2а
Общее уравнение пераболы y=ax^2 +bx +с
Подставим координаты данных точек:
7=а+в+с
17=4а+2в+с
Подставим в эти строчки в=2а
7=3а+с
17=8а+с
Вычитаем из второй строчки первую:
5а=10, а=2, в=4, с=1
итак, y=2x^2 +4x +1
из первого условия следует, что вершина лежит на прямой х=-1
то есть -1=-в/2а, в=2а
Общее уравнение пераболы y=ax^2 +bx +с
Подставим координаты данных точек:
7=а+в+с
17=4а+2в+с
Подставим в эти строчки в=2а
7=3а+с
17=8а+с
Вычитаем из второй строчки первую:
5а=10, а=2, в=4, с=1
итак, y=2x^2 +4x +1
Форма ответа
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