Question

二次函数y=ax平方+bx+c的图像经过第一三象限，则a，b，c取值范围为

A. a＞0，b＞0，c＞0 B. a＜0，b＜0，c≤0 C. a＜0，b＜0，c＞0 D.a＞0，b＞0，c≤0

Answer 1

观察答案，存在c是否为0的选项，通过二次函数经过第一三象限，可知c可以等于0，所以答案在B、D中选择。
再考虑到函数的开口方向，即可知道只有当a<0时候，经过第一三象限。所以最终选择B.

Answer 2

A：取a=1,b=1,c=1,发现Δ＜0，始终在x轴上方，不经过第三象限，所以A错
B：取a=-1,b=-1,c=-1,发现Δ＜0，始终在x轴下方，不经过第一象限，所以B错
C：a＜0，b＜0可知开口向下，对称轴小于0，要使图像经过第一三象限，则c＞0，C对
D：取a=1,b=4,c=3,发现两零点（-3，0）（-1，0）且过第一三象限，所以D错
综上，选C

Answer 3

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