The given equation is \( 12x - 6 = 3x^2 - y \). To express this as a quadratic function of \(x\) in terms of \(y\), we can solve for \(y\).

### Step 1: Rearrange the equation
We want to isolate \(y\) on one side of the equation:

\[
y = 3x^2 - 12x + 6
\]

### Final Equation
The quadratic function is:

\[
y = 3x^2 - 12x + 6
\]

This is a quadratic equation in the form \(y = ax^2 + bx + c\), where:
- \(a = 3\)
- \(b = -12\)
- \(c = 6\)

Would you like to explore more about this quadratic function, such as its vertex, roots, or graph?

### Related Questions:
1. What is the vertex of the quadratic function \( y = 3x^2 - 12x + 6 \)?
2. How do you find the axis of symmetry for a quadratic function?
3. What are the roots of this quadratic function using the quadratic formula?
4. How can you graph the quadratic function \( y = 3x^2 - 12x + 6 \)?
5. How do the coefficients \(a\), \(b\), and \(c\) affect the shape and position of the parabola?

#### Tip:
In any quadratic equation, the sign of \(a\) (coefficient of \(x^2\)) determines whether the parabola opens upwards (\(a > 0\)) or downwards (\(a < 0\)).

Understand how to rearrange and solve the quadratic function 12x - 6 = 3x² - y. This step-by-step guide will walk you through the algebraic process, identifying key concepts such as the standard form of a quadratic equation, the role of coefficients, and how to graph the function. Ideal for Grades 9-10 students studying quadratic equations.

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