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Given the equation \( y = 5 \sin\left(\frac{\pi}{4}x - \frac{\pi}{2}\right) + 4 \), let's break down each component of the function:

1. **Amplitude**: This is the coefficient in front of the sine function, which is \( 5 \). So, the amplitude is \( 5 \).

2. **Period**: The period of a sine function is given by \( \frac{2\pi}{B} \), where \( B \) is the coefficient of \( x \) inside the sine function. Here, \( B = \frac{\pi}{4} \). Therefore, the period is:
   \[
   \frac{2\pi}{\frac{\pi}{4}} = 2\pi \times \frac{4}{\pi} = 8.
   \]

3. **Horizontal Shift**: The horizontal shift (or phase shift) is found by solving \( \frac{\pi}{4}x - \frac{\pi}{2} = 0 \). To find the phase shift:
   \[
   \frac{\pi}{4}x - \frac{\pi}{2} = 0,
   \]
   \[
   \frac{\pi}{4}x = \frac{\pi}{2},
   \]
   \[
   x = \frac{\pi}{2} \times \frac{4}{\pi} = 2.
   \]
   Since this is \( -\frac{\pi}{2} \) inside the function, it means the graph is shifted to the **right** by 2 units.

4. **Midline**: The midline of the sine function is given by the constant added outside the sine function, which is \( y = 4 \).

So, the correct answers should be:
- **Amplitude**: \( 5 \)
- **Period**: \( 8 \)
- **Horizontal Shift**: \( 2 \) units to the right
- **Midline**: \( y = 4 \)

It seems the horizontal shift might be the answer you need to adjust to get full credit. 

Would you like more details or have any questions?

### Related Questions:
1. How do you find the period of a sine or cosine function?
2. What is the effect of the horizontal shift on the graph of a sine function?
3. How does changing the amplitude affect the sine graph?
4. How can you identify the midline of a trigonometric function?
5. How do vertical shifts change the properties of a trigonometric graph?

### Tip:
When identifying the horizontal shift (phase shift) of a sine function, always remember it moves in the opposite direction of the sign inside the function.

Given the equation y = 5 sin(π/4 * x - π/2) + 4, determine the amplitude, period, horizontal shift, and midline.

Explore the sine function y = 5 sin(π/4 * x - π/2) + 4 and learn how to determine its amplitude (5), period (8), horizontal shift (2 units to the right), and midline (y = 4). This breakdown covers core trigonometric concepts suitable for Grades 9-12.

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