Answer :
To understand the transformation from the parent quadratic function [tex]\(y = x^2\)[/tex] to the given quadratic function [tex]\(y = (x-2)^2\)[/tex], let's break it down step by step.
1. Parent Function: The parent quadratic function is [tex]\(y = x^2\)[/tex].
2. Given Function: The given function is [tex]\(y = (x-2)^2\)[/tex].
3. Form Analysis: The given function is in the form [tex]\(y = (x - h)^2 + k\)[/tex], where [tex]\(h\)[/tex] and [tex]\(k\)[/tex] represent shifts along the x- and y-axes, respectively. Specifically, [tex]\(h\)[/tex] represents a horizontal shift and [tex]\(k\)[/tex] represents a vertical shift.
4. Determine Horizontal Shift: In the form [tex]\(y = (x - h)^2\)[/tex]:
- The term [tex]\(x - h\)[/tex] shifts the graph of the parent function horizontally.
- If [tex]\(h\)[/tex] is positive, the graph shifts to the right by [tex]\(h\)[/tex] units.
- If [tex]\(h\)[/tex] is negative, the graph shifts to the left by [tex]\(|h|\)[/tex] units.
5. Identify [tex]\(h\)[/tex]: In the given function, [tex]\(y = (x - 2)^2\)[/tex]:
- Here, [tex]\(h = 2\)[/tex].
6. Interpret the Shift: The value [tex]\(h = 2\)[/tex] means:
- This results in a shift to the right by 2 units because [tex]\(h\)[/tex] is positive.
7. Conclusion: The transformation from the parent function [tex]\(y = x^2\)[/tex] to the given function [tex]\(y = (x-2)^2\)[/tex] is a shift to the right by 2 units.
Therefore, the correct description of the transformation is:
- Shift right 2 units
1. Parent Function: The parent quadratic function is [tex]\(y = x^2\)[/tex].
2. Given Function: The given function is [tex]\(y = (x-2)^2\)[/tex].
3. Form Analysis: The given function is in the form [tex]\(y = (x - h)^2 + k\)[/tex], where [tex]\(h\)[/tex] and [tex]\(k\)[/tex] represent shifts along the x- and y-axes, respectively. Specifically, [tex]\(h\)[/tex] represents a horizontal shift and [tex]\(k\)[/tex] represents a vertical shift.
4. Determine Horizontal Shift: In the form [tex]\(y = (x - h)^2\)[/tex]:
- The term [tex]\(x - h\)[/tex] shifts the graph of the parent function horizontally.
- If [tex]\(h\)[/tex] is positive, the graph shifts to the right by [tex]\(h\)[/tex] units.
- If [tex]\(h\)[/tex] is negative, the graph shifts to the left by [tex]\(|h|\)[/tex] units.
5. Identify [tex]\(h\)[/tex]: In the given function, [tex]\(y = (x - 2)^2\)[/tex]:
- Here, [tex]\(h = 2\)[/tex].
6. Interpret the Shift: The value [tex]\(h = 2\)[/tex] means:
- This results in a shift to the right by 2 units because [tex]\(h\)[/tex] is positive.
7. Conclusion: The transformation from the parent function [tex]\(y = x^2\)[/tex] to the given function [tex]\(y = (x-2)^2\)[/tex] is a shift to the right by 2 units.
Therefore, the correct description of the transformation is:
- Shift right 2 units
