Sketching a parabola from vertex form (a=1)

Task goals

• Read the vertex (h, k) and the axis of symmetry x = h directly from a parabola in vertex form y = (x - h)^2 + k.
• State whether the parabola opens up or down and whether it has a minimum or maximum, and find the minimum y-value.
• Write the equation of a parabola in vertex form given its vertex, or given its axis of symmetry and minimum value.
• Evaluate y for a given x-value, and use symmetry about the vertex to explain why two different x-values give the same y-value.
• Find the y-intercept of a vertex-form parabola by substituting x = 0, and find its x-intercepts by solving (x - h)^2 + k = 0.
• Determine, from the sign of k, whether a vertex-form parabola has zero, one, or two x-intercepts, and justify the reasoning.
• Form a parabola's equation in vertex form from its roots or from its vertex and one other point, and convert between vertex form and factorised form.
• Find an unknown parameter (h or k) in a vertex-form equation given a point on the graph or a known root.