Calculate the coordinates of the intersection points of the parabola y = 3x ^ 2 +2 and the line y = -6x + 2.

The graphs have common points only if the equation consisting of functions equated to each other has a solution, therefore:

3 * x² + 2 = -6 * x + 2,

3 * x² + 6 * x = 0,

3 * x * (x + 2) = 0,

x = 0,

x = -2.

Those. line and parabola intersect at two points, the coordinates of which are:

x = 0, y = 3 * x² + 2 = 2;

x = -2, y = 3 * (-2) ² + 2 = 12 + 2 = 14.

Answer: two points of intersection: (0; 2), (-2; 14).