Step 1:

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Rotation formula :

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If the x and y-axes are rotated through an angle $\"\"$ , the coordinates $\"\"$ of a point P relative to the xy-plane and the coordinates $\"\"$ of the same point relative to the new x and y-axis and are related by the formulas $\"\"$ and $\"\"$ .

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The general form is $\"\"$

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The angle is $\"\"$ .

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Step 2 :

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The equation is $\"\"$ .

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Compare $\"\"$ with $\"\"$

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$\"\"$ and $\"\"$ .

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The angle is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$

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$\"\"$

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Since $\"\"$ . the angle lies in second quadrant.

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$\"\"$

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Step 3 :

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Rotation of x-axis :

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$\"\"$ .

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Substitute $\"\"$ in above equation.

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$\"\"$

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Rotation of y-axis :

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$\"\"$ .

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Substitute $\"\"$ in above equation.

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$\"\"$

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The rotation formulas are $\"\"$ and $\"\"$ .

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Step 4 :

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Complete the square.

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$\"\"$

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This equation is the standard form of the parabola.

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Step 5:

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(1) Draw the coordinate plane.

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(2) Draw the rotated coordinate plane.

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The graph of the function $\"\"$ .

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$\"\"$

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Solution :

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The angle is $\"\"$

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The function $\"\"$ .

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The graph of the function :

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$\"\"$