如图，抛物线y=x 2 +bx+c与x轴交于A（-1，0）、B（3，0）两点，直线L与抛物线交于A、C两点，其中C点的横 如图，抛物线y=x2+bx+c与x轴交于A（-1，0）、B（...
\u5982\u56fe,\u629b\u7269\u7ebfy=-x^2+bx+c\u4e0ex\u8f74\u4ea4\u4e8ea(1,0),b(-3,0)\u4e24\u70b9,1.
\u4f9d\u9898\u610f\u77e5\uff0cx1=1\uff0cx2=-3\u662f\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b-x^2+bx+c=0\u7684\u4e24\u4e2a\u5b9e\u6570\u6839
\u5219\uff1a
x1+x2=-2=b
x1*x2=-3=-c
\u6240\u4ee5\uff0cb=-2\uff0cc=3
\u5219\uff0c\u629b\u7269\u7ebf\u89e3\u6790\u5f0f\u4e3a\uff1ay=-x^2-2x+3
2.
\u7531(1)\u77e5\uff0cy=-x^2-2x+3\uff0c\u5219x=0\u65f6\uff0cy=3
\u6240\u4ee5\uff0c\u70b9C(0,3)
\u4e14\uff0c\u629b\u7269\u7ebf\u5bf9\u79f0\u8f74\u4e3ax=-b/2a=-1
\u25b3QAC\u7684\u5468\u957f=QA+QC+AC\uff0c\u5176\u4e2dAC\u957f\u5ea6\u4e00\u5b9a\uff0c\u90a3\u4e48\u5f53QA+QC\u6700\u5c0f\u65f6\uff0c\u25b3QAC\u7684\u5468\u957f\u8fbe\u5230\u6700\u5c0f
\u56e0\u4e3aA\u3001B\u4e24\u70b9\u5173\u4e8e\u5bf9\u79f0\u8f74x=-1\u5bf9\u79f0\uff0c\u5219QA=QB
\u6240\u4ee5\uff0cQA+QC=QB+QC
\u90a3\u4e48\uff0c\u5f53Q\u3001B\u3001C\u4e09\u70b9\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\u65f6\uff0cQB+QC=BC\u4e3a\u6700\u5c0f
\u5df2\u77e5\u70b9B(-3,0)\uff0cC(0,3)
\u6240\u4ee5\uff0c\u8fc7B\u3001C\u7684\u76f4\u7ebf\u4e3a\uff1ay=x+3
\u90a3\u4e48\u5b83\u4e0e\u5bf9\u79f0\u8f74x=-1\u7684\u4ea4\u70b9\u4e3ay=-1+3=2
\u5373\uff0c\u5b58\u5728\u70b9Q(-1,2)\u4f7f\u5f97\u25b3QAC\u5468\u957f\u6700\u5c0f.
3.
\u7531\u524d\u9762\u77e5\uff0cBC\u6240\u5728\u76f4\u7ebf\u4e3ay=x+3\uff0c\u5373x-y+3=0
\u4e14BC=\u221a[(-3-0)^2+(0-3)^2]=3\u221a2
\u8bbe\u7b2c\u4e8c\u8c61\u9650\u4e0a\u6709\u70b9P(a,-a^2-2a+3)\uff08-3\uff1ca\uff1c0\uff09
\u90a3\u4e48\uff0c\u70b9P\u5230\u76f4\u7ebfx-y+3=0\u7684\u8ddd\u79bb\u3010\u5373\u25b3PBC\u4e2dBC\u8fb9\u4e0a\u7684\u9ad8h\u3011\u4e3a\uff1a
d=h=|a-(-a^2-2a+3)+3|/\u221a[1^2+(-1)^2]
=|a^2+3a|/\u221a2
=-(a^2+3a)/\u221a2
=(-1/\u221a2)*[a^2+3a+(9/4)]+(9/4\u221a2)
=(-1/\u221a2)*[a+(3/2)]^2+(9/4\u221a2)
\u5219\uff0c\u5f53a=-3/2\u65f6\uff0cd\u6709\u6700\u5927\u503c=(9/4\u221a2)
\u6240\u4ee5\uff0cS\u25b3PBC=(1/2)*BC*h=(1/2)*3\u221a2*\uff089/4\u221a2)=27/8
\u6b64\u65f6\uff1a\u70b9P(-3/2,15/4).
\uff081\uff09\u5c06A\uff08-1\uff0c0\uff09\uff0cB\uff083\uff0c0\uff09\u4ee3\u5165y=x2+bx+c\uff0c\u5f97b=-2\uff0cc=-3\uff1b\u2234y=x2-2x-3\uff0e\u5c06C\u70b9\u7684\u6a2a\u5750\u6807x=2\u4ee3\u5165y=x2-2x-3\uff0c\u5f97y=-3\uff0c\u2234C\uff082\uff0c-3\uff09\uff1b\u2234\u76f4\u7ebfAC\u7684\u51fd\u6570\u89e3\u6790\u5f0f\u662fy=-x-1\uff0e\uff082\uff09\u8bbeP\u70b9\u7684\u6a2a\u5750\u6807\u4e3ax\uff08-1\u2264x\u22642\uff09\uff0c\u5219P\u3001E\u7684\u5750\u6807\u5206\u522b\u4e3a\uff1aP\uff08x\uff0c-x-1\uff09\uff0cE\uff08x\uff0cx2-2x-3\uff09\uff1b\u2235P\u70b9\u5728E\u70b9\u7684\u4e0a\u65b9\uff0cPE=\uff08-x-1\uff09-\uff08x2-2x-3\uff09=-x2+x+2\uff0c\u2234\u5f53x=12\u65f6\uff0cPE\u7684\u6700\u5927\u503c=94\uff0e\uff083\uff09\u5b58\u57284\u4e2a\u8fd9\u6837\u7684\u70b9F\uff0c\u5206\u522b\u662fF1\uff081\uff0c0\uff09\uff0cF2\uff08-3\uff0c0\uff09\uff0cF3\uff084+7\uff0c0\uff09\uff0cF4\uff084-7\uff0c0\uff09\uff0e\u2460\u5982\u56fe\uff0c\u8fde\u63a5C\u4e0e\u629b\u7269\u7ebf\u548cy\u8f74\u7684\u4ea4\u70b9\uff0c\u2235C\uff082\uff0c-3\uff09\uff0cG\uff080\uff0c-3\uff09\u2234CG\u2225X\u8f74\uff0c\u6b64\u65f6AF=CG=2\uff0c\u2234F\u70b9\u7684\u5750\u6807\u662f\uff08-3\uff0c0\uff09\uff1b\u2461\u5982\u56fe\uff0cAF=CG=2\uff0cA\u70b9\u7684\u5750\u6807\u4e3a\uff08-1\uff0c0\uff09\uff0c\u56e0\u6b64F\u70b9\u7684\u5750\u6807\u4e3a\uff081\uff0c0\uff09\uff1b\u2462\u5982\u56fe\uff0c\u6b64\u65f6C\uff0cG\u4e24\u70b9\u7684\u7eb5\u5750\u6807\u5173\u4e8ex\u8f74\u5bf9\u79f0\uff0c\u56e0\u6b64G\u70b9\u7684\u7eb5\u5750\u6807\u4e3a3\uff0c\u4ee3\u5165\u629b\u7269\u7ebf\u4e2d\u5373\u53ef\u5f97\u51faG\u70b9\u7684\u5750\u6807\u4e3a\uff081\u00b17\uff0c3\uff09\uff0c\u7531\u4e8e\u76f4\u7ebfGF\u7684\u659c\u7387\u4e0e\u76f4\u7ebfAC\u7684\u76f8\u540c\uff0c\u56e0\u6b64\u53ef\u8bbe\u76f4\u7ebfGF\u7684\u89e3\u6790\u5f0f\u4e3ay=-x+h\uff0c\u5c06G\u70b9\u4ee3\u5165\u540e\u53ef\u5f97\u51fa\u76f4\u7ebf\u7684\u89e3\u6790\u5f0f\u4e3ay=-x+4+7\uff0e\u56e0\u6b64\u76f4\u7ebfGF\u4e0ex\u8f74\u7684\u4ea4\u70b9F\u7684\u5750\u6807\u4e3a\uff084+7\uff0c0\uff09\uff1b\u2463\u5982\u56fe\uff0c\u540c\u2462\u53ef\u6c42\u51faF\u7684\u5750\u6807\u4e3a\uff084-7\uff0c0\uff09\uff1b\u7efc\u5408\u56db\u79cd\u60c5\u51b5\u53ef\u5f97\u51fa\uff0c\u5b58\u57284\u4e2a\u7b26\u5408\u6761\u4ef6\u7684F\u70b9\uff0e
| (1)抛物线的解析式y=x 2 -2x-3，直线AC的函数解析式是y=-x-1；（2）PE的最大值= ； （3）F点的坐标是（-3，0），（1，0），（4- ，0），（4+ ，0）. 扩展阅读：由抛物线y x 2与直线y x ... sin x-y ... 求抛物线y x 2 ... y2 4x ... 抛物线y 2 8x ... 求解方程计算器 ... sinαcosβ ... sinnπ x ... sinx诱导公式大全 ... 本站交流只代表网友个人观点，与本站立场无关 |
