Axis of Symmetry in Factored Form Quadratic

This GeoGebra example dynamically illustrates the axis of symmetry for a quadratic function expressed in factored form y=a(x-p)(x-q). It demonstrates that the axis of symmetry is the vertical line x=(p+q)/2, exactly midway between the two real roots (x-intercepts), and verifies this using the vertex (extremum). The construction employs the Intersect command to find the roots root1 and root2, the Extremum command to locate the vertex E, and the Line command to draw the symmetry axis g, along with auxiliary points F, G, h, i and text labels text1 for annotation. This resource is ideal for upper middle school or high school students learning about quadratic symmetry, root relationships, and the connection between algebraic form and geometric graph. It also serves as an effective classroom demonstration tool for teachers to visually explain the factored form's key properties.