TMUA 2022 Paper 1 Q12 — Worked Solution

P1·Functions, Transformations & Graphs, Differentiation·6.5Official · 2022 · Q12

completing-the-squarelocus-of-verticesminimisation

A family of quadratic curves is given by

y_{k} = 2 (x - \frac{k}{2})^{2} + \frac{k ^{2}}{2} + 4 k + 3

where

k

is any real number and

y_{k}

is a function of

x

.All these curves are sketched, and the point with the lowest

y

-coordinate among all the curves

y_{k}

(a, b)

.Find the value of

a + b

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