Question

Match each function formula with the corresponding transformation of the parent function y = (x - 1)2 1. y = - (x - 1)2 Translated up by 1 unit 2. y = (x - 1)2 + 1 Translated left by 4 units 3. y = (x + 1)2 Translated right by 1 unit 4. y = (x - 2)2 Translated down by 3 units 5. y = (x - 1)2 - 3 Reflected over the x-axis 6. y = (x + 3)2 Reflected over the y-axis

Answer 1

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Explanation:

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Answer 2

1.
`y = - (x - 1)^(2)`, Reflected over the x-axis.

2.
`y = (x - 1)^(2) +1` , Translated up by 1 unit.

3.
`y = (x + 1)^(2)` , Reflected over y-axis

4.
`y = (x - 2)^(2)` ,Translated right by 1 unit.

5.
`y = (x - 1)^2 - 3`, Translated down by 3 units

6.
`y = (x + 3)^2`, Translated left by 4 units.

Explanation:

Given that:

Parent function:
`y = (x - 1)^(2)` Please refer to attached Graph4.

1.
`y = - (x - 1)^(2)` Sign of y is changed from + to -, so it gets reflected over x axis. Please refer to attached Graph3.

2.
`y = (x - 1)^(2) +1`: 1 is added to y to translated up (positive y by 1 unit). Please refer to attached Graph3.

3.
`y = (x + 1)^(2)` , Reflected over y-axis, please refer to attached Graph4.

4.
`y = (x - 2)^(2)` : 1 is subtracted from x , it gets Translated right by 1 unit. Please refer to attached Graph5.

5.
`y = (x - 1)^2 - 3`, 3 subtracted from y so it getss translated down by 3 units. Please refer to attached Graph6.

6.
`y = (x + 3)^2`, 4 added to x, so it gets translated left by 4 units. Please refer to attached Graph5.