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The image appears to show a math problem about finding the vertex form of a parabola. The problem states:

"To turn the function \(y = x^2 + 6x\) into vertex form, you can rewrite it as \(y = (x + 3)^2 - 9\). Then, lower the parabola left and right by 2 units to complete where the new vertex and axis of symmetry are."

Let's go through how to complete the square to rewrite the given equation \(y = x^2 + 6x\) into vertex form and find the vertex and axis of symmetry.

### Step-by-Step Solution

1. **Original Equation:** \(y = x^2 + 6x\)

2. **Complete the Square:**
   - Add and subtract the square of half the coefficient of \(x\) inside the equation:
   - Half of 6 is 3, and \(3^2 = 9\).
   - Rewrite the equation: \(y = x^2 + 6x + 9 - 9\)
   - Factor the perfect square: \(y = (x + 3)^2 - 9\)

3. **Adjusting for Vertex Shift:**
   - According to the instructions, lower the parabola left and right by 2 units. This suggests shifting the graph vertically.
   - So, adjust \(y = (x + 3)^2 - 9\) by adding or subtracting the required amount to shift the graph.

   If it's a vertical shift:
   - Lowering it means subtracting 2: \(y = (x + 3)^2 - 9 - 2 = (x + 3)^2 - 11\).

4. **Vertex Form of the Equation:**
   - Now, \(y = (x + 3)^2 - 11\) is in vertex form.
   - **Vertex:** \((-3, -11)\)
   - **Axis of Symmetry:** \(x = -3\)

Let me know if you would like any further details or have any questions!

### Follow-up Questions:
1. How do you identify the vertex from a parabola in vertex form?
2. What are the steps to find the axis of symmetry of a parabola?
3. Can you describe the effect of shifting a parabola vertically or horizontally?
4. What would happen to the vertex if you shifted the parabola by a different amount?
5. How can completing the square help in graphing quadratic functions?

### Tip:
Completing the square is a powerful technique for converting standard quadratic equations into vertex form, making it easier to identify key features like the vertex and axis of symmetry.

To turn the function y = x^2 + 6x into vertex form, you can rewrite it as y = (x + 3)^2 - 9. Then lower the parabola left and right by 2 units to complete where the new vertex and axis of symmetry are.

Learn how to convert the quadratic equation y = x^2 + 6x into vertex form using completing the square. This step-by-step guide will also show you how to identify the vertex and axis of symmetry. Perfect for students in Grades 8-10.

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