Which statement is true about the axis of symmetry in relation to the vertex?

Which statement is true about the axis of symmetry in relation to the vertex?

• A. The vertex is not on the axis of symmetry.
• B. The axis of symmetry is a horizontal line.
• C. The axis of symmetry passes through the vertex.
• D. The x-intercept is always on the axis.

Answer: (C)

The axis of symmetry is the line that divides a parabola into two mirror-image halves. It always runs through the vertex, no matter which way the parabola opens (vertical or horizontal orientation). So the vertex lies on that axis, which makes the statement true. The axis isn’t inherently horizontal, and the x-intercept isn’t guaranteed to lie on the axis—only in special cases where the axis happens to cross the x-axis at the intercept.

The axis of symmetry is the line that divides a parabola into two mirror-image halves. It always runs through the vertex, no matter which way the parabola opens (vertical or horizontal orientation). So the vertex lies on that axis, which makes the statement true. The axis isn’t inherently horizontal, and the x-intercept isn’t guaranteed to lie on the axis—only in special cases where the axis happens to cross the x-axis at the intercept.