Question

Please help what is the equation for the following graph A=1

Answer 1

Answer:

$f(x)=\sqrt{x+5}-3$

Step-by-step explanation:

Given function for graph: $f(x)=\sqrt{x-h}+k$

Therefore, the parent function is $f(x)=\sqrt{x}$

$f(x)=\sqrt{x-h}+k$ can be obtained by translating $f(x)=\sqrt{x}$ to $h$ units to the right and $k$ units up

The x and y intercept of $f(x)=\sqrt{x}$ is the origin

Therefore, this graph has been translated 5 units to the left and 3 units down.

Therefore, $h=-5$ and $k=-3$

Substituting these values into the given function:

$\implies f(x)=\sqrt{x-(-5)}+(-3)$

$\implies f(x)=\sqrt{x+5}-3$