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電子課本網(wǎng) 第17頁(yè)

第17頁(yè)

信息發(fā)布者:
解:?$(1)$?將點(diǎn)?$A(3,$??$0)$?代入得?$-3^2+2×3+m=0$?
∴?$m=3$?
?$(2)$?∵二次函數(shù)?$y=-x^2+2x+3$?的對(duì)稱軸為直線?$x=1$?
∴另外一個(gè)交點(diǎn)為?$B(-1,$??$0)$?
?$(3)$?以?$AB$?為底,若?$S_{△ABD}=S_{△ABC}$?
則點(diǎn)?$C、$??$D$?到直線?$AB$?的距離相等
若設(shè)?$D(x,$??$y),$?則?$y=±3$?
當(dāng)?$y=3$?時(shí),?$-x^2+2x+3=3,$?解得?$x_{1}=0、$??$x_{2}=2$?
∴?$D_{1}(2,$??$3)$?
當(dāng)?$y=-3$?時(shí),?$-x^2+2x+3=-3,$?解得?$x_{3}=1+\sqrt{7}、$??$x_{4}=1-\sqrt{7}$?
∴?$D_{2}(1+\sqrt{7},$??$-3)、$??$D_{3}(1-\sqrt{7},$??$-3)$?
綜上所述,點(diǎn)?$D$?的坐標(biāo)為?$D_{1}(2,$??$3)、$??$D_{2}(1+ \sqrt{7},$??$-3)、$??$D_{3}(1- \sqrt{7},$??$-3)$?
B
解:?$(1)$?由題意可聯(lián)立方程組?$\begin{cases}{y_{1}=-x^2+2x+3}\\{y_{2}=-x+3}\end{cases}$?
?$-x^2+2x+3=-x+3$?
?$x^2-3x=0$?
?$x_1= 0 ,$??$x_2=3$?
令?$x=0,$??$y_{1}=y_{2}=3;$?令?$x=3,$??$y_{1}=y_{2}=0$?
∴這兩個(gè)函數(shù)的圖像有交點(diǎn),交點(diǎn)坐標(biāo)為?$(0,$??$3)、$??$(3,$??$0)$?
?$(2)0<x<3$?