Are quadratic function graphs symmetrical with respect to their axis of symmetry?

Are quadratic function graphs symmetrical with respect to their axis of symmetry?

• A. Yes
• B. No
• C. Sometimes
• D. Not at all

Answer: (A)

Parabolas always have a vertical line of symmetry through their vertex. For any quadratic function in standard form y = ax^2 + bx + c with a ≠ 0, the graph is a parabola that mirrors itself across the vertical line x = -b/(2a). In vertex form y = a(x - h)^2 + k, this line is x = h. This means for every point at x = h + t there is a matching point at x = h − t with the same y-value, so the left and right sides match perfectly. Because of this, the graph is symmetric about its axis of symmetry for all quadratics. The other options would imply no symmetry or conditional symmetry, which doesn’t fit how a parabola behaves.

Parabolas always have a vertical line of symmetry through their vertex. For any quadratic function in standard form y = ax^2 + bx + c with a ≠ 0, the graph is a parabola that mirrors itself across the vertical line x = -b/(2a). In vertex form y = a(x - h)^2 + k, this line is x = h. This means for every point at x = h + t there is a matching point at x = h − t with the same y-value, so the left and right sides match perfectly. Because of this, the graph is symmetric about its axis of symmetry for all quadratics. The other options would imply no symmetry or conditional symmetry, which doesn’t fit how a parabola behaves.