Question

4 the graph of a quadratic function is shown on the grid. which equation best represents the axis of symmetry? a ( y = 4 ) b ( x = 2 ) c ( x = 0 ) d ( y = 6 )

Explanation:

Step1: Recall axis of symmetry for parabola

The axis of symmetry of a parabola (graph of quadratic function) is a vertical line (if the parabola opens up or down) that passes through the vertex. The equation of a vertical line is of the form \(x = h\), where \(h\) is the x - coordinate of the vertex.

Step2: Identify the vertex's x - coordinate

From the graph, the vertex of the parabola (the highest point) has an x - coordinate of 2. So the axis of symmetry is the vertical line passing through \(x = 2\).

Step3: Eliminate other options

• Option A: \(y = 4\) is a horizontal line, not a vertical line (axis of symmetry for a vertical parabola is vertical), so A is incorrect.
• Option C: \(x = 0\) is the y - axis, but the vertex is not on the y - axis, so C is incorrect.
• Option D: \(y = 6\) is a horizontal line, not a vertical line, so D is incorrect.

Answer:

B. \(x = 2\)