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

If two graphs intersect, then x and y found by the two formulas for the point of their intersection will be the same.

3 * x ^ 2 + 2 = – 6 * x + 2;

3 * x ^ 2 = – 6 * x;

x * (x + 2) = 0;

x1 = 0 or x2 = – 2.

Let’s consider both cases.

If x is 0, then the ordinate of this point is:

y1 = 3 * 0 + 2 = 2.

If x is (- 2), then the ordinate of this point is:

y2 = – 6 * (- 2) + 2 = 12 + 2 = 14.

This means that the data parabola and the straight line intersect at two points with coordinates (0; 2); (- 2; 14).

Answer: (0; 2); (- 2; 14).