https://file.aiquickdraw.com/mathbot/file/17241613744651bi7kk78.jpg

The image shows a problem involving the quadratic equation. From what I can see, you are asked to identify the axis of symmetry and the vertex from the given quadratic function in the form of \( y = ax^2 + bx + c \), and there's a graph provided. 

To convert the quadratic equation into **vertex form** \( y = a(x-h)^2 + k \), we will use the method of completing the square.

### Let's break it down:

1. **Write the quadratic equation**: Based on the image, the equation seems to be in standard form. I cannot read it clearly from the image, so could you provide the specific quadratic equation in the standard form \( y = ax^2 + bx + c \)?

2. **Convert to vertex form**: Once you provide the equation, we can complete the square or use the vertex formula \( x = -\frac{b}{2a} \) to determine the vertex \( (h, k) \), and then rewrite the equation in the vertex form.

Let me know the exact equation, and I'll walk you through the solution!

Would you like to try converting the equation yourself, or do you need further assistance?

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Here are 5 questions you might find interesting after solving this:

1. How does completing the square help in converting to vertex form?
2. What is the significance of the vertex in a parabola?
3. How does the axis of symmetry relate to the vertex?
4. How can you determine the direction of the parabola from the vertex form?
5. How do the coefficients in vertex form \( y = a(x-h)^2 + k \) affect the graph?

**Tip**: Always double-check your work when completing the square, especially with signs and constants.

Learn how to convert a quadratic equation from standard form to vertex form using the method of completing the square. This detailed solution covers identifying the vertex and axis of symmetry, and their significance in parabolic graphs. Suitable for high school students.

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