1. **State the problem:** We are given two functions: the parent function $y=\sqrt{x}$ and a transformed function $y=a\sqrt{b(x-h)}+k$. We need to identify which equation among the options matches the transformed graph that starts near $(5,-5)$ and curves downward. 2. **Recall the transformation formula:** The general form is $y=a\sqrt{b(x-h)}+k$ where: - $h$ is the horizontal shift (right if positive, left if negative), - $k$ is the vertical shift (up if positive, down if negative), - $a$ controls vertical stretch and reflection (if $a$ is negative, the graph reflects over the x-axis), - $b$ controls horizontal stretch or compression. 3. **Analyze the graph description:** - The transformed graph starts near $(5,-5)$, so the horizontal shift $h=5$ and vertical shift $k=-5$. - The graph bends downward, indicating a reflection over the x-axis, so $a$ is negative. - The inside of the square root is $(x - h)$, so it should be $(x - 5)$. 4. **Check each option:** - A) $y = -\sqrt{x - 5} - 5$ matches $a=-1$, $h=5$, $k=-5$ and reflection downward. - B) $y = -\sqrt{x + 5} - 5$ has $h=-5$, which does not match the shift to the right. - C) $y = \sqrt{-(x - 5)} - 5$ changes the inside sign, which affects the domain and shape differently. - D) $y = \sqrt{-(x + 5)} - 5$ also changes the inside sign and shift incorrectly. 5. **Conclusion:** The correct equation is option A. **Final answer:** $\boxed{y = -\sqrt{x - 5} - 5}$