https://file.aiquickdraw.com/mathbot/file/1729203796515dmy9fhx6.jpg

The question in the image asks to determine the transformation of the parabola \( y = x^2 - 6 \) when it is rotated 90° around the origin \( O(0,0) \).

### Steps to solve:
1. **Original Equation:**
   The original parabola equation is:
   \[
   y = x^2 - 6
   \]

2. **Rotation Formula:**
   To rotate a point \((x, y)\) by 90° counterclockwise around the origin, the transformation is:
   \[
   x' = -y
   \]
   \[
   y' = x
   \]
   Here, \(x'\) and \(y'\) are the new coordinates after the rotation.

3. **Substituting the new coordinates:**
   Replace \(x\) with \(y'\) and \(y\) with \(-x'\) in the original equation \(y = x^2 - 6\). This becomes:
   \[
   -x' = (y')^2 - 6
   \]
   Simplifying this, we get:
   \[
   x' = 6 - (y')^2
   \]

4. **New Equation of the Parabola:**
   After the rotation, the equation of the parabola is:
   \[
   x' = 6 - y'^2
   \]

This is the new equation of the parabola after a 90° counterclockwise rotation around the origin.

Would you like further details on this, or have any questions? Here are some additional questions that can expand on this concept:

1. What would the equation be if the parabola was rotated by 180° around the origin?
2. How does the parabola change visually after a 90° rotation?
3. What happens to the vertex of the parabola after rotation?
4. How do we derive rotation formulas for angles other than 90°?
5. How does a clockwise rotation differ from a counterclockwise one in terms of the equation?

**Tip:** When rotating geometric shapes, always remember that a counterclockwise rotation by 90° around the origin results in the transformation \((x, y) \rightarrow (-y, x)\).

Tentukan peta parabola y = x^2 - 6 jika dirotasi pada titik O(0,0) sejauh 90°

This problem explains how to rotate the parabola y = x^2 - 6 by 90 degrees around the origin using coordinate transformation. Suitable for high school students, this lesson involves algebra and the concept of rotating conic sections.

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