Дана квадратичная функция \(\displaystyle y=-3x^2{\small .}\) Вычислите значения функции в заданных точках:
| \(\displaystyle x\) | \(\displaystyle -1\) | \(\displaystyle -0{,}8\) | \(\displaystyle -0{,}6\) | \(\displaystyle -0{,}4\) | \(\displaystyle -0{,}2\) | \(\displaystyle 0\) | \(\displaystyle 0{,}2\) | \(\displaystyle 0{,}4\) | \(\displaystyle 0{,}6\) | \(\displaystyle 0{,}8\) | \(\displaystyle 1\) |
| \(\displaystyle \small y=-3x^2\) |
Выберите график с точками, лежащими на этой квадратичной функции \(\displaystyle y=-3x^2{\small :}\)
| \(\displaystyle \rm I\) | \(\displaystyle \rm II\) |
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| \(\displaystyle \rm III\) | \(\displaystyle \rm IV\) |
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Вычислим значения квадратичной функции \(\displaystyle y=-3x^2\) в заданных точках:
| \(\displaystyle x\) | \(\displaystyle -1\) | \(\displaystyle -0{,}8\) | \(\displaystyle -0{,}6\) | \(\displaystyle -0{,}4\) | \(\displaystyle -0{,}2\) | \(\displaystyle 0\) | \(\displaystyle 0{,}2\) | \(\displaystyle 0{,}4\) | \(\displaystyle 0{,}6\) | \(\displaystyle 0{,}8\) | \(\displaystyle 1\) |
| \(\displaystyle y=-3x^2\) | \(\displaystyle -3\) | \(\displaystyle -1{,}92\) | \(\displaystyle -1{,}08\) | \(\displaystyle -0{,}48\) | \(\displaystyle -0{,}12\) | \(\displaystyle 0\) | \(\displaystyle -0{,}12\) | \(\displaystyle -0{,}48\) | \(\displaystyle -1{,}08\) | \(\displaystyle -1{,}92\) | \(\displaystyle -3\) |
Отметим точки
\(\displaystyle (-1;\, -3),\, (-0{,}8;\, -1{,}92),\, (-0{,}6;\, -1{,}08),\, (-0{,}4;\, -0{,}48),\,(-0{,}2;\, -0{,}12),\, (0;\, 0),\)
\(\displaystyle (0{,}2;\, -0{,}12),\, (0{,}4;\, -0{,}48),\, (0{,}6;\, -1{,}08),\, (0{,}8;\, -1{,}92),\, (1;\, -3)\)
на координатной плоскости:
Сравнивая с данными графиками
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| \(\displaystyle \rm III\) | \(\displaystyle \rm IV\) |
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видим, что график \(\displaystyle \rm IV\) соответствует нашей квадратичной функции \(\displaystyle y=-3x^2{\small .}\)
Ответ: \(\displaystyle \rm IV {\small .}\)