Найти расстояние между началом координат и вершиной параболы y=-x^2+10x-13
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АлгебраАвтор:
phoenixpaulНайдем координаты вершины параболы.
По формуле координаты вершины параболы y=ax^2+bx+c будут , т.е получаем что х=5. Подставляем теперь в уравнение параболы это значение х, получаем: у=-5^2+50-13=12. Координаты вершины будут: (5;12)
Расстояние между точкой с координатами (х,у) и началом координат вычисляется по формуле:
, значит получаем что d=
Ответ: d=13
Автор:
jaceyvia2x0=-b/2a=-10/(-2)=5, y0=-25+50-13=12, т.е. координаты вершины (5, 12)
Найдем расстояние по формуле длины отрезка через координаты его концов. Так как начало координат (0; 0), то расстояние равно sqrt(144+25)=sqrt169=13
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