Question

Найдите координаты вершины параболы у=3х^2-12х+1можно рисунок параболы пж Помагите срочно дам 100б​

Answer 1

Ответ:

В решении.

Объяснение:

Найдите координаты вершины параболы:

у = 3х² - 12х + 1;

1) Найти х₀:

Формула: х₀ = -b/2a;

x₀ = 12/6

х₀ = 2;

2) Найти у₀:

у = 3х² - 12х + 1;

у₀ = 3 * 2² - 12 * 2 + 1 = 12 - 24 + 1 = -11

у₀ = -11;

Координаты вершины параболы: (2; -11).

3) Построить график.

Уравнение квадратичной функции, график - парабола со смещённым центром, ветви направлены вверх.

Придать значения х, подставить в уравнение, вычислить у, записать в таблицу.

           у = 3х² - 12х + 1;

                Таблица:

х  0     1     2     3     4

у   1    -8   -11    -8     1

По вычисленным точкам построить параболу.

Answer 2

Finding the Coordinates of the Vertex of the Parabola

To find the coordinates of the vertex of the parabola given by the equation y = 3x^2 - 12x + 1, we can use the formula for the x-coordinate of the vertex, which is given by x = -b/(2a), where a is the coefficient of the x^2 term and b is the coefficient of the x term in the quadratic equation y = ax^2 + bx + c. Once we have the x-coordinate of the vertex, we can substitute it back into the original equation to find the y-coordinate.

Calculating the Coordinates

Using the formula x = -b/(2a), we can find the x-coordinate of the vertex:

a = 3 (coefficient of x^2 term) b = -12 (coefficient of x term)

Substitute these values into the formula: x = -(-12)/(2*3) x = 2

Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x = 2 back into the original equation:

y = 3(2)^2 - 12(2) + 1 y = 3(4) - 24 + 1 y = 12 - 24 + 1 y = -11

Coordinates of the Vertex

Therefore, the coordinates of the vertex of the parabola y = 3x^2 - 12x + 1 are (2, -11).

Graph of the Parabola

Here's a rough sketch of the parabola: ``` ^ | | | | | | | | * | * | * -----*-----------------> ```

The vertex of the parabola is at the point (2, -11).

I hope this helps! Let me know if there's anything else you'd like to know.