Find the coordinates of the points of intersection of the parabola y = 3x ^ 2 – 48 with the abscissa axis.

A parabola may have one or two intersection points with the Ox axis, or may not intersect with it at all.

If the points of intersection of the parabola y = 3x ^ 2 – 48 with the abscissa axis are, then the coordinates in them are equal to zero. Using this, we get the equation for calculating the x coordinates of the intersection points:

3x ^ 2 – 48 = 0.

Factor out the common factor 3:

3 (x ^ 2 – 16) = 0.

The product is 0 when one of its factors is 0, therefore:

x ^ 2 – 16 = 0;

x ^ 2 = 16;

x1 = 4;

x2 = -4.

Thus, the parabola y = 3x ^ 2 – 48 with the abscissa axis has two intersection points: (4; 0) and (-4; 0).

Answer: (4; 0) and (-4; 0).