Find the coordinates of the intersection points of the graphs of the function y = x ^ 2 and y = 7x-12.

Let us find the abscissas of the points of intersection of the graphs of these functions y = x ^ 2 and y = 7x – 12.

To do this, solve the following equation:

x ^ 2 = 7x – 12.

Solving this quadratic equation, we get:

x ^ 2 – 7x + 12 = 0;

x = (7 ± √ (7 ^ 2 – 4 * 12)) / 2 = (7 ± √ (49 – 48)) / 2 = (7 ± √1) / 2 = (7 ± 1) / 2;

x1 = (7 + 1) / 2 = 8/2 = 4;

x2 = (7 – 1) / 2 = 6/2 = 3.

Find the ordinates of the intersection points of the graphs of these functions:

y1 = 7×1 – 12 = 7 * 4 – 12 = 28 – 12 = 16;

y2 = 7×2 – 12 = 7 * 3 – 12 = 21 – 12 = 9.

Answer: the coordinates of the intersection points of the graphs of these functions (4; 16) and (3; 9).