Final answer:
To find the equation of a secant line passing through two points, we can use the slope-intercept form. Plug in the x-values into the function to get the y-values. Calculate the slope using the formula and find the y-intercept using the slope and one of the given points. Finally, write the equation of the line using the slope and y-intercept.
Step-by-step explanation:
To find the equation of the secant line passing through the points (2, f(2)) and (2h, f(2h)), we first need to find the corresponding y-values for these points. We can plug in the x-values into the function f(x) = 3x² - 2x - 2 to find the y-values. For the point (2, f(2)), we get f(2) = 3(2)² - 2(2) - 2 = 12. For the point (2h, f(2h)), we get f(2h) = 3(2h)² - 2(2h) - 2 = 6h² - 4h - 2.
Next, we can use the formula for the equation of a secant line, which is given by the slope-intercept form y = mx + b. The slope (m) can be found by calculating the difference in y-values and the difference in x-values: m = (f(2h) - f(2)) / (2h - 2). Plugging in the values, we have m = (6h² - 4h - 2 - 12) / (2h - 2) = 6h² - 4h - 14 / 2h - 2.
Finally, we can plug the slope and any one of the given points into the equation y = mx + b to find the y-intercept (b). Let's use the point (2, f(2)), giving us 12 = m(2) + b. Substituting the value of m and solving for b, we get b = 12 - (6h² - 4h - 14) = 4h² + 4h + 2.
Therefore, the equation of the secant line passing through the points (2, f(2)) and (2h, f(2h)) is y = (6h² - 4h - 14) / (2h - 2) * x + (4h² + 4h + 2).