Question

Rewrite y = Square root 25x-75)+3 to make it easy to graph using a translation. Describe the graph

please explain work

Answer 1

The given function is
`y= √(25x-75)+3`
The parent function of the given function is
`√(x)`
So, the given function will be written as following :

`y= √(25x-75)+3` ⇒⇒ add (-3) to both sides


`y-3= √(25(x-3))` ⇒⇒ take 25 as common from 25x and 75

`y-3= √(25) √((x-3))` ⇒⇒ bring 25 outside the square root

`y-3= \ 5 √((x-3))`

`y = \ 5 √((x-3)) +3`

So, the given function can be graphed easily from the parent function √x
By translation √x from (0,0) to point (3,3), then dilated with factor 5
See the attached figure
Parent function √x ⇒⇒⇒ with blue color
The given function ⇒⇒⇒ with red color

So, The answer is
`y = \ 5 √((x-3)) +3`