The diagram shows the graph of $y = a(x + b)(x + c)(x + d)^2.$ What are possible values of a, b, c and d? A - HSC - SSCE Mathematics Extension 1 - Question 6 - 2018 - Paper 1

The coefficient 'a' affects the vertical stretch or compression. We can observe from the sketch that the graph opens downwards, indicating that 'a' must be negative. Additionally, the squared term $(x + d)^2$ suggests 'd' should be positioned such that it corresponds to the minimum point.

Through the provided options, check for consistency with the properties analyzed:

• Option A: Results in an incorrect sign for 'a'.
• Option B: Disregarded for similar reasons as A.
• Option C: Matches the conditions with $a = -3$ confirming a downward opening and proper position of the other roots.
• Option D: Incorrect sign for 'b'. Thus, the correct values from the options must be from Option C: $a = -3, b = -2, c = -1, d = 1$.