Final answer:
To find the points of intersection of the two given functions, set them equal to each other, combine like terms, and use the quadratic formula. Solve for x and then substitute back into the original functions to find the corresponding y-values, rounding to three decimal places.
Step-by-step explanation:
To find the points of intersection of the graphs of the functions f(x) = 0.2x² - 1.3x - 3 and g(x) = -0.2x² + 1.1x + 8.1, we set the two functions equal to each other and solve for x:
0.2x² - 1.3x - 3 = -0.2x² + 1.1x + 8.1.
Combining like terms:
0.2x² + 0.2x² - 1.3x - 1.1x - 3 - 8.1 = 0
0.4x² - 2.4x - 11.1 = 0.
Using the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), where a = 0.4, b = -2.4, and c = -11.1, we solve for the values of x that satisfy the equation.
The solutions to this equation are the x-values of the points of intersection, which can then be substituted back into either original function to find the corresponding y-values, completing the coordinates of the intersection points. Round these answers to three decimal places as requested.