Solved on Dec 14, 2023

Describe the transformations for the quadratic $f(x) = (x-3)^2 + 2$ . Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

STEP 1

Assumptions
1. The given quadratic function is $f(x) = (x-3)^2 + 2$ .
2. We need to describe the transformations applied to the parent function $f(x) = x^2$ to obtain the given function.

STEP 2

Identify the parent function.
The parent function for a quadratic is $f(x) = x^2$ .

STEP 3

Compare the given function to the parent function.
The given function is $f(x) = (x-3)^2 + 2$ . We will compare this to $f(x) = x^2$ to identify the transformations.

STEP 4

Identify the horizontal shift.
The term $(x-3)$ in the given function indicates a horizontal shift. If the term inside the parentheses is $(x-h)$ , it represents a shift to the right by $h$ units. If it is $(x+h)$ , it represents a shift to the left by $h$ units.

STEP 5

Determine the direction and magnitude of the horizontal shift.
Since the term is $(x-3)$ , we have a shift to the right by 3 units.

STEP 6

Identify the vertical shift.
The constant term $+2$ outside the squared term in the given function indicates a vertical shift.

STEP 7

Determine the direction and magnitude of the vertical shift.
Since the constant term is $+2$ , we have a shift upwards by 2 units.

STEP 8

Combine the identified transformations.
The given function $f(x) = (x-3)^2 + 2$ is the result of shifting the parent function $f(x) = x^2$ three units to the right and two units up.

STEP 9

Select the correct transformation from the given options.
The correct transformation is "Three units to the right, and two units up."
The transformations for the quadratic function $f(x) = (x-3)^2 + 2$ are three units to the right, and two units up.

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Describe the transformations for the quadratic $f(x) = (x-3)^2 + 2$ . Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

STEP 1

Assumptions
1. The given quadratic function is $f(x) = (x-3)^2 + 2$ .
2. We need to describe the transformations applied to the parent function $f(x) = x^2$ to obtain the given function.

STEP 2

Identify the parent function.
The parent function for a quadratic is $f(x) = x^2$ .

STEP 3

Compare the given function to the parent function.
The given function is $f(x) = (x-3)^2 + 2$ . We will compare this to $f(x) = x^2$ to identify the transformations.

STEP 4

Identify the horizontal shift.
The term $(x-3)$ in the given function indicates a horizontal shift. If the term inside the parentheses is $(x-h)$ , it represents a shift to the right by $h$ units. If it is $(x+h)$ , it represents a shift to the left by $h$ units.

STEP 5

Determine the direction and magnitude of the horizontal shift.
Since the term is $(x-3)$ , we have a shift to the right by 3 units.

STEP 6

Identify the vertical shift.
The constant term $+2$ outside the squared term in the given function indicates a vertical shift.

STEP 7

Determine the direction and magnitude of the vertical shift.
Since the constant term is $+2$ , we have a shift upwards by 2 units.

STEP 8

Combine the identified transformations.
The given function $f(x) = (x-3)^2 + 2$ is the result of shifting the parent function $f(x) = x^2$ three units to the right and two units up.

STEP 9

Select the correct transformation from the given options.
The correct transformation is "Three units to the right, and two units up."
The transformations for the quadratic function $f(x) = (x-3)^2 + 2$ are three units to the right, and two units up.

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Describe the transformations for the quadratic f(x)=(x−3)2+2f(x) = (x-3)^2 + 2f(x)=(x−3)2+2. Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

STEP 1

Assumptions1. The given quadratic function is f(x)=(x−3)2+2 f(x) = (x-3)^2 + 2 f(x)=(x−3)2+2.2. We need to describe the transformations applied to the parent function f(x)=x2 f(x) = x^2 f(x)=x2 to obtain the given function.

STEP 2

Identify the parent function.The parent function for a quadratic is f(x)=x2 f(x) = x^2 f(x)=x2.

STEP 3

Compare the given function to the parent function.The given function is f(x)=(x−3)2+2 f(x) = (x-3)^2 + 2 f(x)=(x−3)2+2. We will compare this to f(x)=x2 f(x) = x^2 f(x)=x2 to identify the transformations.

STEP 4

STEP 5

Determine the direction and magnitude of the horizontal shift.Since the term is (x−3) (x-3) (x−3), we have a shift to the right by 3 units.

STEP 6

Identify the vertical shift.The constant term +2 +2 +2 outside the squared term in the given function indicates a vertical shift.

STEP 7

Determine the direction and magnitude of the vertical shift.Since the constant term is +2 +2 +2, we have a shift upwards by 2 units.

STEP 8

Combine the identified transformations.The given function f(x)=(x−3)2+2 f(x) = (x-3)^2 + 2 f(x)=(x−3)2+2 is the result of shifting the parent function f(x)=x2 f(x) = x^2 f(x)=x2 three units to the right and two units up.

STEP 9

Select the correct transformation from the given options.The correct transformation is "Three units to the right, and two units up."The transformations for the quadratic function f(x)=(x−3)2+2 f(x) = (x-3)^2 + 2 f(x)=(x−3)2+2 are three units to the right, and two units up.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Describe the transformations for the quadratic $f(x) = (x-3)^2 + 2$ . Shift left 2 units and up 3 units, left 3 units and up 2 units, right 3 units and down 2 units, or right 3 units and up 2 units.

Assumptions
1. The given quadratic function is $f(x) = (x-3)^2 + 2$ .
2. We need to describe the transformations applied to the parent function $f(x) = x^2$ to obtain the given function.

Identify the parent function.
The parent function for a quadratic is $f(x) = x^2$ .

Compare the given function to the parent function.
The given function is $f(x) = (x-3)^2 + 2$ . We will compare this to $f(x) = x^2$ to identify the transformations.

Determine the direction and magnitude of the horizontal shift.
Since the term is $(x-3)$ , we have a shift to the right by 3 units.

Identify the vertical shift.
The constant term $+2$ outside the squared term in the given function indicates a vertical shift.

Determine the direction and magnitude of the vertical shift.
Since the constant term is $+2$ , we have a shift upwards by 2 units.

Combine the identified transformations.
The given function $f(x) = (x-3)^2 + 2$ is the result of shifting the parent function $f(x) = x^2$ three units to the right and two units up.

Select the correct transformation from the given options.
The correct transformation is "Three units to the right, and two units up."
The transformations for the quadratic function $f(x) = (x-3)^2 + 2$ are three units to the right, and two units up.