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

1.
y = - (x - 1)2
translated right by 1 unit

2.
y = (x - 1)2 + 1
reflected over the y-axis

3.
y = (x + 1)2
translated left by 4 units

4.
y = (x - 2)2
translated up by 1 unit

5.
y = (x - 1)2 - 3
translated down by 3 units

6.
y = (x + 3)2
reflected over the x-axis

Always remember general rules of transformation.

1) Vertical Shift:

y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.

2) Horizontal Shift:

y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.

3) Reflection across x-axis

y= - f(x) ; reflect the graph of f across the x-axis.

Now,

The parent function is y= -(x+2)²

1. y= -(x+4)²

In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²

So, according to rule 2 it will shift the parent function to the left by 2 units.

E is the correct option.

2. y = - (x + 2)² - 2

In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2

So, according to rule 1, it will shift the graph down by 2 units.

F is the correct option.

3. y=(x - 2)²

In this question, two operations are performed on the parent function.

First one, -4 is added with x+2 so we get x+2-4= x-2

Second one, -1 is multiplied with parent function.

By performing the two operations at a time we get a new function which is

y=-(-(x+2-4)²)=(x-2)²

The first operation will translate the parent function 4 units right (according to rule 2).

The second operation will reflect the graph across x-axis(according to rule 3).

D and translation 4 units to right is correct option.

4. y= 2 -(x+2)²

In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.

C is the correct option.

5. y= -x²

In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²

So, according to rule 2 it will shift the graph right by 2 units.

B is the correct option.

6. y= (x+2)²

In this question, -1 is multiplied with parent function and we get

y= -(-(x+2)²)= (x+2)²

So, according to rule 3 , graph is reflected across x-axis.

D is the correct answer.

The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).

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Step-by-step explanation: