Question

move at least one of the 3 guide points below to complete the graph of $y = \sqrt{x + 2}$. 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

Explanation:

Step1: Find the domain vertex

The parent function is $y=\sqrt{x}$, with vertex at $(0,0)$. For $y=\sqrt{x+2}$, set $x+2=0$, so $x=-2$. The vertex (blue point) is $(-2, 0)$.

Step2: Find first red point

Choose $x=-1$:
$y=\sqrt{-1+2}=\sqrt{1}=1$.
Point: $(-1, 1)$

Step3: Find second red point

Choose $x=2$:
$y=\sqrt{2+2}=\sqrt{4}=2$.
Point: $(2, 2)$

Answer:

1. Move the blue vertex point to $(-2, 0)$
2. Move the first red point to $(-1, 1)$
3. Move the second red point to $(2, 2)$

This will complete the correct graph of $y=\sqrt{x+2}$.