The graph of a sinusoidal function has a minimum point at (0,10) and then has a maximum point at (2,-4). Write the formula of the function, where X is entered in radians.

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Identify Amplitude: Identify the amplitude of the sinusoidal function. The amplitude (A) is half the distance between the maximum and minimum values of the function. The maximum value is -4 and the minimum value is 10, so the amplitude is (10 - (-4))/2 = 14/2 = 7.Determine Vertical Shift: Determine the vertical shift (D) of the sinusoidal function. The vertical shift is the average of the maximum and minimum values. So, D = (10 + (-4))/2 = 6/2 = 3.Calculate Period: Calculate the period (T) of the sinusoidal function. Since the function goes from a minimum at x=0 to a maximum at x=2, half of the period is 2. Therefore, the full period T is 2 * 2 = 4 radians.Find Horizontal Shift: Find the horizontal shift (C) of the sinusoidal function. Since the minimum occurs at x=0, the horizontal shift C is 0.Determine Reflection: Determine the reflection of the sinusoidal function. Since the function goes from a minimum to a maximum as x increases, it is a reflection of the standard sine function. This means we will use a negative amplitude.Write Sinusoidal Function: Write the formula of the sinusoidal function. The general form of a sinusoidal function is y = A * sin(B(x - C)) + D, where B = 2π/T. Since we have a reflection, A is negative. Plugging in the values we have: A = -7, B = 2π/4 = π/2, C = 0, and D = 3. So the formula is y = -7 * sin((π/2)x) + 3.

The graph of a sinusoidal function has a minimum point at $(0,10)$ and then has a maximum point at $(2,-4)$ . Write the formula of the function, where $X$ is entered in radians.

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The graph of a sinusoidal function has a minimum point at (0,10)(0,10)(0,10) and then has a maximum point at (2,−4)(2,-4)(2,−4). Write the formula of the function, where XXX is entered in radians.

The graph of a sinusoidal function has a minimum point at $(0,10)$ and then has a maximum point at $(2,-4)$ . Write the formula of the function, where $X$ is entered in radians.