### Equation of a Semi-Circle **Task:** Find the equation of the semi-circle pictured. **Graph Description:** The graph displays a semi-circle centered at the point \((-3, 3)\) on a coordinate plane. The semi-circle extends from \((-5, 3)\) to \((-1, 3)\) on the x-axis, with its arc reaching up to \(y = 1\). This semi-circle is oriented such that it opens downwards. **Steps to Find the Equation:** 1. **Identify the Center:** The center of the semi-circle is at \((-3, 3)\). 2. **Determine the Radius:** The distance from the center to the edge along the x-axis is 2 units, indicating that the radius is 2. 3. **Equation of a Semi-Circle:** For a semicircle opening downwards with the center at \((h, k)\) and radius \(r\), the standard form of the equation is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Given: - \(h = -3\) - \(k = 3\) - \(r = 2\) 4. **Plug in the Values:** \[ (x + 3)^2 + (y - 3)^2 = 2^2 \] 5. **Simplified Equation:** \[ (x + 3)^2 + (y - 3)^2 = 4 \] **Note:** This represents the full circle. To express the equation for only the upper half (semi-circle), solve for \(y\) in terms of \(x\) for the top half: \[ y = 3 - \sqrt{4 - (x + 3)^2} \] **Input Box:** An input box is provided to enter the equation. After inputting the equation, you can click the "Submit Question" button. **URL Source (not clickable):** `https://www.myopenmath.com/assess2/#/skip/9`