To convert the quadratic equation \( y = x^2 + 12x \) into vertex form, we'll complete the square. The vertex form of a quadratic equation is:

\[
y = a(x-h)^2 + k
\]

where \((h, k)\) is the vertex of the parabola.

### Steps:
1. Start with the given equation:
   \[
   y = x^2 + 12x
   \]
   
2. Complete the square by taking half of the coefficient of \(x\) (which is 12), squaring it, and adding and subtracting that value inside the equation:
   \[
   \text{Half of 12} = 6, \quad 6^2 = 36
   \]
   Add and subtract 36 inside the equation:
   \[
   y = (x^2 + 12x + 36) - 36
   \]
   
3. Rewrite the trinomial as a perfect square:
   \[
   y = (x + 6)^2 - 36
   \]

So, the vertex form of the equation is:

\[
y = (x + 6)^2 - 36
\]

### Vertex:
The vertex is \((-6, -36)\).

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. How can you determine the vertex from the standard form of a quadratic equation?
2. What does completing the square mean geometrically?
3. How do you convert a quadratic equation into factored form?
4. How do the values of \(h\) and \(k\) affect the graph of the parabola?
5. What is the axis of symmetry of the parabola, and how do you find it?

**Tip:** The vertex of a parabola in standard form \( ax^2 + bx + c \) can also be found using the formula \( x = -\frac{b}{2a} \).

Learn how to convert the quadratic equation y = x² + 12x into vertex form by completing the square. This step-by-step guide covers key algebraic concepts and formulas, including how to find the vertex and rewrite the equation. Suitable for students in Grades 8-10.

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