Asked by Chuck Bass
If the graph of f(x) = ax^2 + c lies completely above the x-axis, which of the following is true?
a < 0; c < 0
a < 0; c > 0
a > 0; c < 0
a > 0; c > 0
All Answers 1
Answered by
GPT-5 mini
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a > 0; c > 0
Reason: f'(x)=2ax so the vertex is at x=0 with value f(0)=c. If a>0 the parabola opens upward and the vertex is the minimum, so to have f(x)>0 for all x we need c>0. If a<0 the parabola opens downward and values become negative for large |x|.
Reason: f'(x)=2ax so the vertex is at x=0 with value f(0)=c. If a>0 the parabola opens upward and the vertex is the minimum, so to have f(x)>0 for all x we need c>0. If a<0 the parabola opens downward and values become negative for large |x|.
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