At what values of x are the points of the graph of the function y = x ^ 2-2x-8 located above the Ox axis?

1. To find the values of the variable at which the points of the graph of the function y = x ^ 2 – 2x – 8 are located above the abscissa axis, we solve the strict inequality:

x ^ 2 – 2x – 8> 0; (one)

D / 4 = (b / 2) ^ 2 – ac;
D / 4 = 1 ^ 2 + 8 = 9;
x = (-b / 2 ± √ (D / 4)) / a;
x = (1 ± √9) / 1 = 1 ± 3;
x1 = 1 – 3 = -2;
x2 = 1 + 3 = 4.
2. The first coefficient is greater than zero, therefore, inequality (1) is satisfied by the external, with respect to two roots, intervals:

x ∈ (-∞; -2) ∪ (4; 2).

Answer: (-∞; -2) ∪ (4; 2).