The equation of a parabola is y=x^2+8x+6. Write the equation in vertex form.

To rewrite the quadratic equation \( y = x^2 + 8x + 6 \) in **vertex form** \( y = a(x - h)^2 + k \), we need to complete the square.

### Steps to complete the square:

1. Start with the given equation:
   \[
   y = x^2 + 8x + 6
   \]
2. Focus on the \( x^2 + 8x \) part. To complete the square, take half of the coefficient of \( x \), which is \( 8 \), and square it:
   \[
   \left(\frac{8}{2}\right)^2 = 16
   \]
3. Add and subtract 16 inside the equation (so we don't change its value):
   \[
   y = (x^2 + 8x + 16) - 16 + 6
   \]
4. Now, factor the perfect square trinomial \( x^2 + 8x + 16 \):
   \[
   y = (x + 4)^2 - 10
   \]

### Final result:
The equation in vertex form is:
\[
y = (x + 4)^2 - 10
\]

The vertex of the parabola is at \( (-4, -10) \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the significance of the vertex form of a parabola?
2. How do you find the axis of symmetry from the vertex form?
3. Can you explain how the vertex form helps in graphing a parabola?
4. What other methods can be used to find the vertex of a parabola?
5. How does the vertex relate to the minimum or maximum point of the parabola?

**Tip:** In vertex form, the value \( h \) represents the x-coordinate of the vertex, and \( k \) represents the y-coordinate.

Learn how to convert the quadratic equation y = x^2 + 8x + 6 into vertex form by completing the square. Follow this step-by-step guide that simplifies key algebraic concepts. Suitable for Grades 9-11 students.

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