Sqrt Curve Equation 1Ddae0

1. **State the problem:** We need to find the equation of a square-root function that passes through the points $(-1, -2)$ and $(0, -1)$. 2. **General form of square-root function:** The equation can be written as $$y = a\sqrt{x - h} + k$$ where $(h, k)$ is the starting point (the vertex) of the curve, and $a$ controls the vertical stretch or compression. 3. **Identify the vertex:** The graph starts at $(-1, -2)$, so we set $h = -1$ and $k = -2$. Thus, the equation becomes $$y = a\sqrt{x + 1} - 2$$ 4. **Use the second point to find $a$:** Substitute $(x, y) = (0, -1)$ into the equation: $$-1 = a\sqrt{0 + 1} - 2$$ $$-1 = a\cdot 1 - 2$$ $$-1 + 2 = a$$ $$a = 1$$ 5. **Final equation:** Substitute $a = 1$ back into the equation: $$y = \sqrt{x + 1} - 2$$ **Answer:** The equation of the graph is $$y = \sqrt{x + 1} - 2$$.