Answer:
f(x) = 6 * sin(2x) - 10
Explanation:
We can use the given information to write the general formula of a sinusoidal function as follows:
f(x) = A * sin(B(x - C)) + D
The amplitude of the function, A, is equal to the difference between the maximum and minimum values of the function, which in this case is -10 - (-4) = 6.
The period of the function, B, is equal to the distance between consecutive maximum or minimum points, which in this case is 2 - 0 = 2.
The phase shift of the function, C, is equal to the horizontal shift of the entire function, which in this case is 0 since the minimum point is at x = 0.
The vertical shift of the function, D, is equal to the y-coordinate of the minimum point, which in this case is -10.
Therefore, the formula of the given function is:
f(x) = 6 * sin(2(x - 0)) - 10
We can simplify this formula by removing the unnecessary parentheses and constants:
f(x) = 6 * sin(2x) - 10
This is the final formula for the given sinusoidal function, where x is entered in radians.