TMUA Official 2022 Paper 1 · Question 12

Official papers

Official 2022 Paper 1 · Q12

Paper 1Functions & graphsAlgebra

A family of quadratic curves is given by

y_k=2\left(x-\frac k2\right)^2+\frac{k^2}2+4k+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 $y_k$ is $(a,b)$ .

Find the value of $a+b$ .

-1

-3

-5

-7

-9

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