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Let's solve part **b** of the problem.

### Problem:
Write down the equation of the line of symmetry for the graph of \( y = 2x^2 - 8x + 1 \).

### Solution:
The equation of the line of symmetry (also called the axis of symmetry) for a quadratic function in the form \( y = ax^2 + bx + c \) is given by:

\[
x = -\frac{b}{2a}
\]

For the given quadratic equation \( y = 2x^2 - 8x + 1 \):

- \( a = 2 \)
- \( b = -8 \)

Substituting these values into the formula:

\[
x = -\frac{-8}{2(2)} = \frac{8}{4} = 2
\]

### Final Answer:
The equation of the line of symmetry is \( x = 2 \).

Would you like more details or have any questions about this solution?

Here are some related questions you might find interesting:
1. How do you find the vertex of a parabola given a quadratic equation?
2. What is the significance of the axis of symmetry in the graph of a quadratic function?
3. How do you convert a quadratic function to its vertex form?
4. What does the discriminant of a quadratic equation tell you about its roots?
5. How can you find the roots of a quadratic equation using the quadratic formula?

**Tip:** When working with quadratic functions, always check if completing the square can simplify the process of finding the vertex and the axis of symmetry.

Express 2x^2 - 8x + 5 in the form a(x + b)^2 + c, where a, b, and c are integers. Write down the equation of the line of symmetry for the graph of y = 2x^2 - 8x + 1.

Learn how to express 2x^2 - 8x + 5 in vertex form using completing the square and write down the equation of the line of symmetry for the graph of y = 2x^2 - 8x + 1. This step-by-step solution covers quadratic equations, symmetry, and algebra for students in Grades 8-10.

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