1.7: Complete the square and find a maximum

4PM1/2/June/2021 — Question 2 · 6 marks

f(x)=2+45x−125x2.f(x)=2+\frac{4}{5}x-\frac{1}{25}x^2.
Given that f(x)\displaystyle f(x) can be expressed in the form
A−B(x+C)2,A-B(x+C)^2,
where A\displaystyle A, B\displaystyle B and C\displaystyle C are constants,
(a) find the value of A\displaystyle A, the value of B\displaystyle B and the value of C\displaystyle C.
(4)
(b) Hence write down
(i) the maximum value of f(x)\displaystyle f(x),
(ii) the value of x\displaystyle x for which this maximum occurs.
(2)