1.1: Modulus and quadratic: sketch, solve and inequality

0606/11/M/J/17 — Question 8 · 11 marks

(i)
On the axes below, sketch the graphs of y=∣2x−5∣y = |2x - 5| and 9y=80x−16x29y = 80x - 16x^{2}.
[5]
(ii)
Solve ∣2x−5∣=4|2x - 5| = 4.
[3]
(iii)
Hence show that the graphs of y=∣2x−5∣y = |2x - 5| and 9y=80x−16x29y = 80x - 16x^{2} intersect at the points where y=4y = 4.
[1]
(iv)
Hence find the values of xx for which 9∣2x−5∣≤80x−16x29|2x - 5| \le 80x - 16x^{2}.
[2]