Final answer:
The coordinates of the turning point of the curve are (4, -29).
Step-by-step explanation:
To find the coordinates of the turning point (also known as the vertex) of the quadratic equation y = -x² - 8x + 19, we can use the formula x = -b/2a. In this equation, a = -1, b = -8, and c = 19. Plugging in these values, we get x = -(-8)/(2*(-1)) = 4.
To find the corresponding y-coordinate, substitute this value of x back into the original equation: y = -4² - 8(4) + 19 = -16 - 32 + 19 = -29. Therefore, the coordinates of the turning point of the curve are (4, -29).