Question 5:给我讲解分析思路和证明
It is given that (2x + 3) is one of the factors of f(x) = x (5 – 2x) + m, such that m is a constant.
(a) Find the value of m. [3 marks]
(b) By using the method of completing the square, express f(x) in the form, f(x) = a(x – h)2 + k, such that a, h and k are constants.
Hence, sketch the graph of f(x) for 0 ⩽ x ⩽ 4.
[4 marks]
(c) Using the same axes in (b), sketch and label the graph of g(x) = (a – 1)(x – h)2 + k.
[1 mark]