Question

graph the equation shown below by transforming the given graph of the parent function.
$y = \sqrt{x + 5} + 2$

Explanation:

Step1: Identify parent function

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

Step2: Find horizontal shift

For $y=\sqrt{x+5}$, shift left 5 units:
New vertex: $(0-5, 0)=(-5,0)$

Step3: Find vertical shift

Add 2, shift up 2 units:
New vertex: $(-5, 0+2)=(-5,2)$

Step4: Transform key points

Parent points: $(0,0), (1,1), (4,2), (9,3)$
Shifted points:
$(-5,2)$, $(-5+1,2+1)=(-4,3)$, $(-5+4,2+2)=(-1,4)$, $(-5+9,2+3)=(4,5)$

Answer:

The graph of $y=\sqrt{x+5}+2$ is the parent square root graph shifted 5 units left and 2 units up, with key points at $(-5,2)$, $(-4,3)$, $(-1,4)$, and $(4,5)$, curving upward to the right from the vertex $(-5,2)$.