For-the quadratic equation `3x^2+12xx+10=0` , what is the .distance between the y-axis and the axis of symmetry of the quadratic graph?

Options

A. 2 units
B. 4 units
C. 3 units
D. 6 units

Answer

To find the distance between the y-axis and the axis of symmetry of the quadratic graph given by the equation \(3x^2 + 12x + 10 = 0\), we will follow these steps:

### Step 1: Identify the coefficients
The standard form of a quadratic equation is \(ax^2 + bx + c = 0\). Here, we have:
- \(a = 3\)
- \(b = 12\)
- \(c = 10\)

### Step 2: Calculate the axis of symmetry
The formula for the axis of symmetry \(x\) for a quadratic equation is given by:
\[ x = -\frac{b}{2a} \]
Substituting the values of \(b\) and \(a\):
\[ x = -\frac{12}{2 \cdot 3} \]
\[ x = -\frac{12}{6} \]
\[ x = -2 \]

### Step 3: Determine the distance from the y-axis
The y-axis is represented by the line \(x = 0\). To find the distance between the y-axis and the axis of symmetry (which is at \(x = -2\)), we calculate the absolute difference:
\[ \text{Distance} = |0 - (-2)| = |0 + 2| = 2 \]

### Conclusion
The distance between the y-axis and the axis of symmetry of the quadratic graph is **2 units**.

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