Question

Функция задана формулой y = x(x -1)

Answer 1

Раскрой скобки, y=x^2-x это парабола с ветвями вверх.

Answer 2

The function you provided is represented by the formula: y = x(x - 1)

This is a quadratic function. It is in the form of y = ax^2 + bx, where a = 1 and b = -1.

The graph of this function will be a parabola. The parabola opens upwards because the coefficient of the x^2 term (a) is positive (a = 1). The vertex of the parabola will be at the point (h, k), where h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

To find the vertex of the parabola, we can use the formula for the x-coordinate of the vertex: h = -b / (2a).

Substitute the values of a and b: h = -(-1) / (2 * 1) = 1 / 2

Now, to find the y-coordinate of the vertex (k), we can substitute the value of h back into the original equation: y = (1/2)(1/2 - 1) = (1/2)(-1/2) = -1/4

So, the vertex of the parabola is at the point (1/2, -1/4).

The axis of symmetry of the parabola is the vertical line passing through the vertex. The equation of the axis of symmetry is x = h, which is x = 1/2 in this case.

The graph of the function y = x(x - 1) will be a parabola that opens upwards and has its vertex at the point (1/2, -1/4). The axis of symmetry is the line x = 1/2.

If you need further information or have any other questions, feel free to ask!