Quadratic Graph

Conditions for a quadratic graph to be always negative when a<0

We know that when the coefficient a is less than 0, the quadratic graph is a frowning curve. In order for this frowning quadratic graph to be always negative, meaning it will always be below the x-axis, what this also means is that the curve does not cut the x-axis. Therefore, to find the condition, we know that discriminant must be less than 0. Solving this inequality will give the answer.

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