1. **State the problem:** We need to graph the function $y = 2\sqrt{x}$ by transforming the parent function $y = \sqrt{x}$. 2. **Parent function:** The parent function is $y = \sqrt{x}$, which is a square root curve starting at the origin $(0,0)$ and increasing slowly to the right. 3. **Transformation rule:** The function $y = 2\sqrt{x}$ means we multiply the output of the parent function by 2. This is a vertical stretch by a factor of 2. 4. **Effect on points:** For example, the parent function passes through points $(1,1)$, $(4,2)$, and $(9,3)$. 5. **Apply transformation:** Multiply the $y$-values by 2: $$ (1,1) \to (1, 2 \times 1) = (1,2) $$ $$ (4,2) \to (4, 2 \times 2) = (4,4) $$ $$ (9,3) \to (9, 2 \times 3) = (9,6) $$ 6. **Graph shape:** The graph still starts at the origin and opens to the right, but it rises twice as fast. **Final answer:** The graph of $y = 2\sqrt{x}$ is a vertical stretch of the parent function $y = \sqrt{x}$ by a factor of 2, passing through points $(1,2)$, $(4,4)$, and $(9,6)$.