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欢迎各位同行指正

抛物线与坐标轴交点 构成的三角形问题. 欢迎各位同行指正. 面积篇. P. 4. C. 3. 2. 1. B. A. O. 2. 例 1: 已知抛物线 y= - x 2 +2x+3 与 x 轴交于 A,B 两点,其中 A 点位于 B 点的左侧,与 y 轴交于 C 点,顶点为 P ,. (1,4). S △ AOC = _______ _______. (0,3). S △ BOC =_______. (-1,0). (3,0). (1,4). (0,3). P. 4. C. 3. 2. (3,0). (-1,0). 1. B.

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欢迎各位同行指正

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  1. 抛物线与坐标轴交点 构成的三角形问题 欢迎各位同行指正

  2. 面积篇

  3. P 4 C 3 2 1 B A O 2 例1:已知抛物线y=-x2+2x+3与x轴交于A,B两点,其中A点位于B点的左侧,与y轴交于C点,顶点为P, (1,4) S△ AOC=______________ (0,3) S△ BOC=_______ (-1,0) (3,0)

  4. (1,4) (0,3) P 4 C 3 2 (3,0) (-1,0) 1 B A O 2 S△ COP=_______ S△ PAB=_______

  5. D E (1,4) P 4 (0,3) C 3 E 2 1 (-1,0) B A F O 2 (3,0) F S△ PCB=_______ S△ ACP=_______

  6. y 3 1 - A O x B C M 在平面直角坐标系中,有两点A(-1,0),B(3,0),如图,小敏发现所有过A,B两点的抛物线如果与y轴负半轴交于点C,M为抛物线的顶点,那么△ACM与△ACB的面积比不变,请你求出这个比值。 (2004绍兴中考题)

  7. y D 3 1 - A O x S△ACB= ×4×3a=6a B C M = ×1×3a+ ×(3a+4a) ×1- ×2×4a =a ∴ 解:设抛物线解析式为y=a(x+1)(x-3), 即y=ax2-2ax-3a,即y=a(x-1)2-4a ∴C点与M点坐标分别是(0,-3a), (1,-4a) ∴S△ACM=S△AOC+S梯形OCMD-S△ADM

  8. 形状篇

  9. Y C A(-1,0) B(3,0) X 问2:在抛物线的解析式 中, 已知:抛物线与x轴的交点坐标为A (-1,0)和B(3,0),若∠ACB=90度. 问1:C点的坐标是多少?

  10. Y 若题设中的A、B两点的坐标未知,而已知∠ACB=90度,你能求出 吗? C D B X A

  11. Y A B X C 1、从上面的探索中我们看到解析式中的△与∠ACB有关,那么你能否进一步找出它俩之间的关系吗? 2、那么如果△ ACB是等边三角形,则△是多少?

  12. 小结

  13. 谢谢

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