Question

move at least one of the 3 guide points below to complete the graph of $y = 2sqrt{x} - 2$. moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x - axis.
reset reflect over x - axis
answer attempt 2 out of 5
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Explanation:

Step1: Identify parent function

Parent function: $y=\sqrt{x}$

Step2: Find transformed key points

For $y=2\sqrt{x}-2$, transform $(\sqrt{x})$ points:

1. $x=0$: $y=2\sqrt{0}-2=-2$ → $(0, -2)$
2. $x=1$: $y=2\sqrt{1}-2=0$ → $(1, 0)$
3. $x=4$: $y=2\sqrt{4}-2=2$ → $(4, 2)$
4. $x=9$: $y=2\sqrt{9}-2=4$ → $(9, 4)$

Step3: Adjust guide points

Move blue point (shift control) to $(0, -2)$. Move red points to $(1, 0)$ and $(4, 2)$ to set vertical stretch.

Answer:

The completed graph of $y=2\sqrt{x}-2$ has key guide points at:

1. Blue shift point: $(0, -2)$
2. Red stretch points: $(1, 0)$ and $(4, 2)$

When plotted, the curve starts at $(0, -2)$, passes through $(1, 0)$ and $(4, 2)$, and increases gradually as $x$ increases.