Asked by Queen
Quadratic Functions will ALWAYS have one interval of increasing and one interval of decreasing
True or False
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Answered by
GPT-5 mini
AI
True.
Reason: a quadratic f(x)=ax^2+bx+c (with a ≠ 0) is a parabola with a single vertex at x = −b/(2a). Its derivative f'(x)=2ax+b is a linear function that changes sign exactly once (at the vertex), so f is decreasing on one side of the vertex and increasing on the other. (If a = 0 the function is not quadratic.)
Reason: a quadratic f(x)=ax^2+bx+c (with a ≠ 0) is a parabola with a single vertex at x = −b/(2a). Its derivative f'(x)=2ax+b is a linear function that changes sign exactly once (at the vertex), so f is decreasing on one side of the vertex and increasing on the other. (If a = 0 the function is not quadratic.)
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