Reading and forming parabolas in vertex form y = a(x - h)^2 + k where a is not 1

Teaching guidance

• Extends sketching a parabola from vertex form (T4_LO17, a = 1 only) to a is not 1: the vertex (h, k) still reads directly from y = a(x - h)^2 + k, and x = h is still the axis of symmetry, but a now also controls whether the parabola opens up (a > 0) or down (a < 0), and whether it is narrower (|a| > 1) or wider (|a| < 1) than y = x^2.
• This page's task decks (OBJECTIVES/lo-graphing-parabolas-a-1) cover: reading off vertex/axis/opening direction/width from vertex form; finding the y-intercept (substitute x = 0); finding two extra symmetric points either side of the axis; solving a(x - h)^2 + k = 0 for the x-intercepts (or explaining why none exist); and, at proficient/excellence tier, working backwards -- given a vertex and one point, or a vertex and both roots -- to write the equation in vertex form, including solving for an unknown a.
• The Master Guide's own citation list for this entry (10MAT-ALGEBRA-SKILLS-GRAPHS-EX03) also lists table-of-values plotting, cubic graphs, reciprocal graphs, and estimating the gradient of a curve -- none of those are covered by this page, which is scoped to vertex-form parabolas only; recorded here as a scope gap for future dedicated LOs if ever built.