Find the coordinates of the intersection points of the graphs of the functions y = x ^ 2-10 and y = 4x + 11.

Find the abscissas of the intersection points of the graphs of these functions y = x ^ 2 -10 and y = 4x + 11.

To do this, solve the following equation:

x ^ 2 – 10 = 4x + 11.

Solving this quadratic equation, we get:

x ^ 2 – 10 – 4x – 11 = 0.

x ^ 2 – 4x – 21 = 0.

x = 2 ± √ (2 ^ 2 + 21) = 2 ± √ (4 + 21) = 2 ± √25 = 2 ± 5;

x1 = 2 – 5 = -3;

x2 = 2 + 5 = 7.

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

y1 = 4×1 + 11 = 4 * (-3) + 11 = -12 + 11 = -1;

y2 = 4×2 + 11 = 4 * 7 + 11 = 28 + 11 = 39.

Answer: the coordinates of the intersection points of the graphs of these functions (-3; -1) and (7; 39).