The vertex at the origin, the axis along the x-axis, and passes through `(-3,6)`.

Answer

To find the equation of the parabola with the given conditions, we can follow these steps:

### Step 1: Understand the Parabola's Orientation
The problem states that the vertex is at the origin (0,0) and the axis is along the x-axis. This indicates that the parabola opens either to the right or to the left. Since it passes through the point (-3, 6), it will open to the left.

### Step 2: Write the Standard Form of the Parabola
For a parabola that opens to the left with its vertex at the origin, the standard form of the equation is:
\[ y^2 = -4ax \]
where \(a\) is the distance from the vertex to the focus.

### Step 3: Substitute the Point into the Equation
We know that the parabola passes through the point (-3, 6). We can substitute \(x = -3\) and \(y = 6\) into the equation to find \(a\):
\[ 6^2 = -4a(-3) \]

### Step 4: Simplify the Equation
Calculating the left side:
\[ 36 = -4a(-3) \]
This simplifies to:
\[ 36 = 12a \]

### Step 5: Solve for \(a\)
Now, we can solve for \(a\):
\[ a = \frac{36}{12} = 3 \]

### Step 6: Write the Final Equation
Now that we have the value of \(a\), we can substitute it back into the standard form of the parabola:
\[ y^2 = -4(3)x \]
This simplifies to:
\[ y^2 = -12x \]

### Final Answer
The equation of the parabola is:
\[ y^2 = -12x \]

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