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Quadratic Equation : Relation Between Parameters a, b and c and Turning Points

Given the curve
y = ax3 + bx2 + cx + d, a ≠ 0
Find the relation between the parameters a, b, and c that will ensure that the curve:
(a) has only one turning point.
(b) has no turning points.
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The relation between prameters a, b and c in a quadratic equation and turning points is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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