Question

How do you translate graphs of square root functions ?

Answer 1

Hint: Take the reference equation as $y=\sqrt{x}$. For horizontal translation add or subtract ‘a’ unit inside the square root function. Similarly, for vertical translation add or subtract ‘a’ unit outside the square root function.
There are two types of translation i.e. Horizontal translation and Vertical translation.
Horizontal translation: This translation is done along the x-axis.

Complete step by step answer:
Let’s consider the equation $y=\sqrt{x}$
For Horizontal translation in the graph, we have an addition or subtraction inside of the square root function i.e. $y=\sqrt{x\pm a}$ where ‘a’ is the horizontal shift.
Subtraction of ‘a’ units moves the graph to the right along the x-axis and addition of ‘a’ units moves the graph to the left along the x-axis.
So, the function $y=\sqrt{x-a}$ is at the right of the function $y=\sqrt{x}$ and the function$y=\sqrt{x+a}$ is at the left of the function $y=\sqrt{x}$.
Vertical translation: The translation is done along the y-axis.
Again considering the equation $y=\sqrt{x}$
For Vertical translation in the graph, we have an addition or subtraction outside of the square root function i.e. $y=\sqrt{x}\pm a$ where ‘a’ is the vertical shift.
Addition of ‘a’ units moves the graph up along the y-axis and subtraction of ‘a’ units moves the graph down along the y-axis.
So, the function $y=\sqrt{x}+a$ is at the top of the function $y=\sqrt{x}$ and the function$y=\sqrt{x}-a$ is at the bottom of the function $y=\sqrt{x}$.
These are the translations of the square root function.

Note:
It should be remembered that in horizontal shifting the graph moves left and right respectively for adding and subtracting ‘a’ units. Similarly in vertical shifting the graph moves up and down respectively for adding and subtracting ‘a’ units.