Through what point of the abscissa axis passes the axis of the parabola y = x ^ 2-4x.

In order to find through which point on the abscissa axis the parabola axis passes, you first need to find the intersection points of the parabola with the abscissa axis. In this regard, we equate y to 0 and solve the resulting equation.

y = 0 then:

x ^ 2 – 4x = 0;

x * (x – 4) = 0.

x1 = 0;

x2 = 4.

We found the coordinates of the points on the abscissa axis. The axis of the parabola passes through the vertex of this parabola and divides it into two equal parts. This means that to find the point of intersection of the parabola axis and the abscissa axis, we need to find the value of x, which will lie in the middle between x1 and x2.

Let’s find this value:

x = (x1 + x2) / 2;

x = (0 + 4) / 2;

x = 2.

Answer: x = 2.