Final answer:
The function y = 2x² - 8x - 10 is positive in the intervals x < -1 and x > 5, which are the intervals outside the roots of the quadratic equation determined by the quadratic formula.
Step-by-step explanation:
The student has asked to identify the intervals on which the function y = 2x² - 8x - 10 is positive. This is a quadratic function, and its graph is a parabola that opens upwards since the coefficient of x² is positive. To determine where the function is positive, we need to find the roots of the equation by setting y to zero and solving for x, which will give us the x-values where the function intersects the x-axis.
Setting the equation to zero we get: 2x² - 8x - 10 = 0. By applying the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), we can find the roots.
Here, a = 2, b = -8, and c = -10. Inserting these values into the quadratic formula provides us with two roots, x = -1 and x = 5. Therefore, the function is positive when x < -1 and x > 5, which corresponds to option B of the multiple-choice selections provided in the original question.