The axis of the parabola `y^(2)+2x=0` is :

Options

A. `x=0`
B. `y=0`
C. `x=2`
D. `y=2`

Answer

To find the axis of the parabola given by the equation \( y^2 + 2x = 0 \), we can follow these steps:

### Step 1: Rewrite the equation
Start by rewriting the equation in a more standard form. We can rearrange the given equation:

\[ y^2 = -2x \]

### Step 2: Identify the standard form of the parabola
The standard form of a parabola that opens to the left or right is given by:

\[ y^2 = 4ax \]

In this case, we have \( y^2 = -2x \). We can compare this with the standard form to identify the value of \( a \).

### Step 3: Find the value of \( a \)
From the equation \( y^2 = -2x \), we can see that:

\[ 4a = -2 \]

To find \( a \), we divide both sides by 4:

\[ a = \frac{-2}{4} = -\frac{1}{2} \]

### Step 4: Determine the axis of the parabola
The axis of a parabola in the form \( y^2 = 4ax \) is the line that passes through the vertex and is parallel to the axis of symmetry. For this parabola, since it opens to the left (as indicated by the negative value of \( a \)), the axis will be the x-axis.

### Step 5: Write the equation of the axis
The equation of the x-axis is:

\[ y = 0 \]

### Conclusion
Thus, the axis of the parabola \( y^2 + 2x = 0 \) is:

\[ \text{Axis: } y = 0 \]

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