Question

Не выполняя построения, найдите координаты точек пересечения с осями координат графика функции y=x2-2x

Answer 1

Найдем пересечение с осью икс:
$x^2-2x=0$ - так как координаты игрека на оси икс, равны всегда нулю.
$x(x-2)=0$
$x_1=0$
$x_2=2$

Имеем координаты:
$(0;0),(2;0)$

2)
Теперь с осью игрек:
$0^2-2*0=y$
$y=0$
Отсюда:
$(0;0)$

Answer 2

Finding the Intersection Points with the Coordinate Axes

To find the coordinates of the points where the graph of the function y = x^2 - 2x intersects the coordinate axes, we need to determine the x and y values when the function equals zero.

1. Intersection with the x-axis (y = 0): - To find the x-coordinate when y = 0, we set the function equal to zero and solve for x: ``` x^2 - 2x = 0 ``` - Factoring out x, we have: ``` x(x - 2) = 0 ``` - Setting each factor equal to zero, we find two possible values for x: ``` x = 0 or x - 2 = 0 ``` - Solving for x, we get: ``` x = 0 or x = 2 ``` - Therefore, the graph intersects the x-axis at the points (0, 0) and (2, 0).

2. Intersection with the y-axis (x = 0): - To find the y-coordinate when x = 0, we substitute x = 0 into the function: ``` y = (0)^2 - 2(0) ``` - Simplifying, we get: ``` y = 0 ``` - Therefore, the graph intersects the y-axis at the point (0, 0).

So, the coordinates of the points where the graph of the function y = x^2 - 2x intersects the coordinate axes are: - Intersection with the x-axis: (0, 0) and (2, 0) - Intersection with the y-axis: (0, 0).

Please let me know if I can help you with anything else.