The graph represents the relation y = x$^2$ - 3x - 3. What is the equation of the line of symmetry of the graph?

Analyze the question: We need the line of symmetry of the parabola y = x² - 3x - 3. A parabola with a vertical axis is symmetric about a vertical line, so the answer has the form x = k.

Concept: For y = ax² + bx + c, the line of symmetry is

x = -b / (2a)

This is the x-coordinate of the turning point (vertex).

Solution:

Here a = 1, b = -3, c = -3.

x = -(-3) / (2 × 1) = 3/2 = 1.5

Check by completing the square:

y = x² - 3x - 3 y = (x - 1.5)² - 2.25 - 3 y = (x - 1.5)² - 5.25

The vertex is at (1.5, -5.25), so the axis of symmetry is x = 1.5. This agrees with the formula.

Eliminating other options:

• A and D are horizontal lines (y = constant). A parabola of this type cannot be symmetric about a horizontal line.
• B (x = 1) is a vertical line, but it does not pass through the vertex.

So the correct answer is C. x = 1.5.

Tip: For any quadratic, the line of symmetry is x = -b/(2a). Also, it sits exactly halfway between the two roots (x-intercepts), if they exist. Options like "y = ..." can be ruled out immediately for a standard upward or downward parabola.