Question

write the equation of the axis of symmetry for this graph.
hint: the axis of symmetry is the vertical line that splits the quadratic directly in half.
\\(x = ?\\)

Explanation:

Identify the vertex of the parabola

To find the axis of symmetry, we first locate the vertex of the parabola on the graph. The vertex is the lowest point (minimum) of this upward-opening parabola. Looking closely at the grid, the lowest point is located at \(x = 2\) and \(y = -2\). Thus, the vertex is \((2, -2)\).

Apply the axis of symmetry definition

Using the Axis of Symmetry concept, the axis of symmetry of a vertical parabola is the vertical line passing through its vertex. For any parabola with a vertex at \((h, k)\), the equation of this vertical line is always given by \(x = h\).

Determine the final equation

Since the \(x\)-coordinate of our vertex is \(h = 2\), the vertical line that splits the parabola directly in half is \(x = 2\).

Answer:

Write the equation of the axis of symmetry for this graph.

Hint: The axis of symmetry is the vertical line that splits the quadratic directly in half.

\(x =\) <blank>2</blank>