Put the equation that is in general form: 𝑦=𝑥2+12𝑥+27
into standard form: 𝑦=(𝑥-ℎ)2+𝑘:

Answer: 𝑦 =

To convert the quadratic equation \( y = x^2 + 12x + 27 \) from its general form to its standard form, we need to complete the square.

### Steps to Complete the Square

1. Start with the given equation:
\[ y = x^2 + 12x + 27 \]

2. Move the constant term to the other side of the equation:
\[ y - 27 = x^2 + 12x \]

3. To complete the square, take the coefficient of \( x \), divide it by 2, and square it. Add and subtract this square inside the equation:
\[ y - 27 = x^2 + 12x + \left(\frac{12}{2}\right)^2 - \left(\frac{12}{2}\right)^2 \]
\[ y - 27 = x^2 + 12x + 36 - 36 \]

4. Rewrite the equation as a perfect square trinomial:
\[ y - 27 = (x + 6)^2 - 36 \]

5. Move the constant term back to the other side of the equation:
\[ y = (x + 6)^2 - 36 + 27 \]
\[ y = (x + 6)^2 - 9 \]

### Standard Form

The equation in standard form \( y = (x - h)^2 + k \) is:
\[ y = (x + 6)^2 - 9 \]

### Answer

\[ y = (x + 6)^2 - 9 \]

Would you like any further details or have any questions?

Here are 5 related questions you might find useful:

1. How do you solve quadratic equations by completing the square?
2. What is the vertex form of a quadratic function, and how is it useful?
3. Can you explain how to find the vertex of a parabola from its standard form?
4. How do you convert a quadratic function from standard form to general form?
5. What are the steps to graph a quadratic function given in standard form?

**Tip:** Completing the square is a useful technique not only for converting to standard form but also for solving quadratic equations and understanding the properties of parabolas.

Learn how to convert the quadratic equation y = x^2 + 12x + 27 from its general form to standard form (y = (x - h)^2 + k) using the method of completing the square. This problem covers key algebraic concepts, including completing the square and the vertex form of a quadratic equation. Suitable for students in Grades 10-12.

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