Match each function formula with the corresponding transformation of the parent function y = (x - 1)2

y = - (x - 1)2 Translated right by 1 unit
y = (x - 1)2 + 1 Translated down by 3 units
y = (x + 1)2 Reflected over the y-axis
y = (x - 2)2 Reflected over the x-axis
y = (x - 1)2 - 3 Translated up by 1 unit
6. y = (x + 3)2 Translated left by 4 units

Reflected over x axis => y=3(-x)
Reflected over y axis => y=-(3x)
Translated down 2 => y=3x-2
Translated right 2 => y=3(x-2)
Translated up 1 => y=3x+1
Translated left 1 => y=3(x+1)
Hope this helps

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ColinJacobus ColinJacobus · Answer 2 · 2019-03-08T03:04:22-05:00

Answer: The answer is given below.

Step-by-step explanation: We are given to match the function formulae with the corresponding transformation of the parent function \(y=(x-1)^2.\)

We know that, if x changes to (x + a), then the graph will move 'a' units left or right depending on 'a' is positive or negative.

Similarly, if y changes to (y + b), then the graph will move 'b' units upwards or downwards depending on 'a' is negative or positive.

The correct matches are as follows:

\((1)~y=-(x-1)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{Reflection across the X-axis}\\\\(2)~y=(x-1)^2+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{Translated up by 1 unit}\\\\(3)~y=(x+1)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{Translated left by 2 units}\\\\(4)~y=(x-2)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{Translated right by 1 unit}\\\\(5)~y=(x-1)^2-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{Translated down by 3 units}\\\\(6)~y=(x+3)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{Translated left by 4 units}.\)