Forming equation of parabolas

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Learning objective overview

Master Teaching Guide coverage for this objective.

Other: Not in Beta Textbook; no verified external resource found (this LO is the reverse skill -- forming the equation from a given vertex or given roots -- and CorbettMaths, Dr Austin Maths's full Non-Linear Graphs practice-grid list, and nzmaths.co.nz all only cover the forward skill of drawing/sketching a parabola from its equation, not this LO's scope)

Given a parabola's vertex, write its equation in vertex form y=(x-h)^2+k.
Given a parabola's two x-intercepts (roots), write its equation in factorised form y=(x-p)(x-q).
Form a parabola's equation from its graph and expand it into standard (expanded) form.
Form a parabola's equation from its graph and state its axis of symmetry.
Write a parabola's equation in vertex form and evaluate it to find y at a given x-value.

Extension pairing with T4_LO16 and T4_LO17: those LOs sketch a parabola given its equation in factorised or vertex form; this LO works in reverse, forming the equation (a=1 only) from given features of the parabola.
Given the two x-intercepts (roots) p and q, the equation is y = (x - p)(x - q) -- write each intercept as its own bracket factor, negating the intercept value.
Given the vertex (h, k), the equation is y = (x - h)^2 + k -- negate the vertex's x-coordinate inside the bracket, keep the y-coordinate as the constant.
Given three points on the parabola (or the y-intercept plus the roots), substitute to check or determine the equation; students should verify a formed equation by substituting the given points back in.