Question

найти координаты вершины параболы y=(x-3)^2 и построить её график! срочно ребят))

Answer 1

парабола, ветви вверх(тк а>0)

вершина (3;0) - сдвиг по оси х на три единицы вправо

Answer 2

Finding the Coordinates of the Vertex of a Parabola

To find the coordinates of the vertex of the parabola given by the equation y = (x - 3)^2, we can use the formula for the x-coordinate of the vertex, which is given by x = -b/2a, where a and b are the coefficients of the quadratic equation.

In this case, the equation is in the form y = ax^2 + bx + c, where a = 1, b = -6, and c = 9. Therefore, the x-coordinate of the vertex is x = -(-6)/(2*1) = 3.

To find the y-coordinate of the vertex, we substitute the x-coordinate back into the equation. So, y = (3 - 3)^2 = 0^2 = 0.

Therefore, the coordinates of the vertex of the parabola y = (x - 3)^2 are (3, 0).

Graphing the Parabola

To graph the parabola y = (x - 3)^2, we can plot a few points and then connect them to form the curve.

Let's choose some x-values and calculate the corresponding y-values:

- When x = 0, y = (0 - 3)^2 = 9. - When x = 1, y = (1 - 3)^2 = 4. - When x = 2, y = (2 - 3)^2 = 1. - When x = 4, y = (4 - 3)^2 = 1. - When x = 5, y = (5 - 3)^2 = 4. - When x = 6, y = (6 - 3)^2 = 9.

Now, we can plot these points on a graph:

| x | y | |---|---| | 0 | 9 | | 1 | 4 | | 2 | 1 | | 3 | 0 | | 4 | 1 | | 5 | 4 | | 6 | 9 |

By connecting these points, we get the graph of the parabola y = (x - 3)^2.


Please note that the graph is symmetric with respect to the vertical line x = 3, which is the axis of symmetry. The vertex (3, 0) lies on this axis.

I hope this helps! Let me know if you have any further questions.