Question

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.

Explanation:

Step1: Identify parent function points

Parent function: $y=\sqrt{x}$. Key points:

• $(0, 0)$
• $(1, 1)$
• $(4, 2)$

Step2: Apply vertical stretch factor

Stretch by factor 2: Multiply y-values by 2:

• $(0, 0\times2)=(0,0)$
• $(1, 1\times2)=(1,2)$
• $(4, 2\times2)=(4,4)$

Step3: Apply vertical shift down

Shift down 2 units: Subtract 2 from y-values:

• $(0, 0-2)=(0,-2)$
• $(1, 2-2)=(1,0)$
• $(4, 4-2)=(4,2)$

Answer:

The key points for $y=2\sqrt{x}-2$ are $(0,-2)$, $(1,0)$, and $(4,2)$. Plot these points and draw the curve starting at $(0,-2)$ and increasing to follow the shape of the transformed square root function.