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The given equation is \( y^2 = -(-1)^2 \times x \).

First, let's simplify the equation:

1. \( (-1)^2 = 1 \), since squaring any real number results in a positive value.
2. Thus, the equation becomes \( y^2 = -1 \times x \), which simplifies to:
   \[
   y^2 = -x
   \]

This is the standard form of a parabola, specifically \( y^2 = -x \). 

### Orientation of the Parabola:
- The general form of a parabola that opens horizontally is \( y^2 = 4px \), where:
  - If \( p > 0 \), the parabola opens to the right.
  - If \( p < 0 \), the parabola opens to the left.

In the simplified equation \( y^2 = -x \), the coefficient of \( x \) is negative, indicating that the parabola opens **to the left**.

### Correct Answer:
- **d. Left**

Would you like further details or have any other questions?

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Here are 5 related questions:
1. What is the vertex of the parabola \( y^2 = -x \)?
2. How does the orientation of the parabola change if the equation is \( y^2 = x \)?
3. How can we determine the focus of the parabola \( y^2 = -4x \)?
4. What is the directrix of the parabola given by the equation \( y^2 = -x \)?
5. How do you convert the given equation \( y^2 = -x \) to its vertex form?

**Tip:** Always check for simplifications in equations to make it easier to identify the orientation and other properties of curves.

Identify the orientation of the given parabola's equation: y^2 = -(-1)^2 x.

Determine the orientation of the parabola given by the equation y^2 = -(-1)^2 x. This problem explores key concepts in quadratic equations and the orientation of parabolas, suitable for students in Grades 10-12.

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