Which of the following is the graph of the curve `sqrt(|y|)=x` is ?

Options

A.
B.
C.
D.

Answer

To solve the problem of finding the graph of the curve given by the equation \(\sqrt{|y|} = x\), we will follow these steps:

### Step 1: Square both sides of the equation
Starting from the equation:
\[ \sqrt{|y|} = x \]
We square both sides to eliminate the square root:
\[ |y| = x^2 \]

### Step 2: Remove the absolute value
The absolute value equation \(|y| = x^2\) can be split into two cases:
1. \(y = x^2\) (when \(y \geq 0\))
2. \(y = -x^2\) (when \(y < 0\))

### Step 3: Analyze the two cases
- For \(y = x^2\):
- This is a parabola that opens upwards and is valid for \(y \geq 0\).

- For \(y = -x^2\):
- This is a parabola that opens downwards and is valid for \(y < 0\).

### Step 4: Sketch the graphs
Now we can sketch both parts of the graph:
- The curve \(y = x^2\) will be drawn in the upper half of the graph (above the x-axis).
- The curve \(y = -x^2\) will be drawn in the lower half of the graph (below the x-axis).

### Step 5: Combine the graphs
The final graph will consist of both curves:
- The upper part is the parabola \(y = x^2\) for \(y \geq 0\).
- The lower part is the parabola \(y = -x^2\) for \(y < 0\).

Thus, the complete graph of the curve \(\sqrt{|y|} = x\) consists of two parabolas, one opening upwards and the other opening downwards.

### Conclusion
The correct option that represents the graph of the curve \(\sqrt{|y|} = x\) is option **b**.

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