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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
Question 6
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. $a = -6, \; b = -2, \; c = -1, \; d = 1$ B. $a = -6... show full transcript
Worked Solution & Example Answer: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
Step 1
Step 2
Analyze the effect of a, b, c, and d
Answer
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 suggests 'd' should be positioned such that it corresponds to the minimum point.
Step 3
Determine possible values
Answer
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 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: .