Sketching a parabola from factorised form (a=1)

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Read the two x-intercepts (roots) directly from a parabola given in factorised form y = (x - p)(x - q), including the repeated-root case y = (x - p)^2.
Find the axis of symmetry of a factorised-form parabola as the midpoint of its two roots, x = (p + q) / 2.
Find the coordinates of the vertex (turning point) by substituting the axis-of-symmetry x-value back into the equation.
Find the y-intercept of a factorised-form parabola by substituting x = 0.
Write a parabola's equation in factorised form given its roots, including a repeated root, and given the axis of symmetry plus one root.
Explain why the axis of symmetry sits halfway between the roots, and identify or correct a student's sign or axis-of-symmetry error made when reading factorised form.
Expand a factorised-form equation and compare factorised form with vertex form, describing an advantage or limitation of each.

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A parabola in factorised form y = (x - p)(x - q) has x-intercepts at x = p and x = q, found by setting each bracket to zero.
The axis of symmetry lies exactly halfway between the two x-intercepts: x = (p + q) / 2. The vertex sits on this axis of symmetry, so substitute its x-value back into the equation to find the y-coordinate of the vertex.
The y-intercept is found by substituting x = 0, giving y = (-p)(-q) = pq.
Since a = 1 is positive, the parabola opens upward: sketch the two x-intercepts, the y-intercept, and the vertex (turning point), then draw a smooth upward-opening curve through them.