The two roots of a quadratic equation are `-6` and 12, what is the distance between the axis of symmetry of the quadratic graph and the Z-axis?

Options

A. 6 units
B. 1 unit
C. 2 units
D. 3 units

Answer

To find the distance between the axis of symmetry of the quadratic graph and the Z-axis, we can follow these steps:

### Step 1: Identify the roots of the quadratic equation
The roots given are -6 and 12.

### Step 2: Calculate the axis of symmetry
The axis of symmetry for a quadratic equation can be calculated using the formula:
\[ x = \frac{\alpha + \beta}{2} \]
where \(\alpha\) and \(\beta\) are the roots of the equation.

Substituting the values:
\[ x = \frac{-6 + 12}{2} = \frac{6}{2} = 3 \]

### Step 3: Determine the position of the Z-axis
The Z-axis is a vertical line that passes through the origin (0,0) and extends vertically. In a 3D coordinate system, the Z-axis is at \(x = 0\).

### Step 4: Calculate the distance from the axis of symmetry to the Z-axis
The distance between two vertical lines \(x = 3\) (axis of symmetry) and \(x = 0\) (Z-axis) can be calculated as:
\[ \text{Distance} = |3 - 0| = 3 \]

### Conclusion
The distance between the axis of symmetry of the quadratic graph and the Z-axis is **3 units**.

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