Question

5-3 graphing radical functions (lms graded)
write the function that describes the graph above.
y = \square (simplify your answer.)
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question 10 of 13

Explanation:

Step1: Identify parent function form

The graph is a square root function, parent form: $y=\sqrt{x-h}+k$, where $(h,k)$ is the vertex.

Step2: Locate vertex from graph

The vertex is at $(-4, -3)$. Substitute $h=-4$, $k=-3$:
$y=\sqrt{x-(-4)}+(-3) = \sqrt{x+4}-3$

Step3: Verify with a point

Test $x=0$: $y=\sqrt{0+4}-3 = 2-3=-1$, which matches the graph's point $(0,-1)$.

Answer:

$\boldsymbol{\sqrt{x+4}-3}$