已知抛物线y=2x平方-6x+5用配方法把它化为y=a(x-h)平方+K的形式,并指出它的开口方向,对称轴和顶点坐标
\u5df2\u77e5\u629b\u7269\u7ebfY=\u8d1f1/2X\u5e73\u65b9+\uff085-M\uff09X+M-3\u7684\u5bf9\u79f0\u8f74\u662fY\u8f74\u6c42\u629b\u7269\u7ebf\u7684\u9876\u70b9\u5750\u6807y=-1/2x²+\uff085-m\uff09x+m-3
a=-1/2 b=5-m c=m-3
\u5f53x=-b/2a=-\uff085-m\uff09/-1 =5-m
y=4ac-b²/4a=4*\uff08-1/2\uff09*\uff08m-3\uff09-\uff085-m\uff09²/4*\uff08-1/2\uff09=-2\uff08m-3\uff09-\uff085-m\uff09²/\uff08-2\uff09
\uff08x\uff0cy\uff09\u4e3a\u30105-m \uff0c-2\uff08m-3\uff09-\uff085-m\uff09²/\uff08-2\uff09\u3011
\u2235\u5b83\u7684\u5bf9\u79f0\u8f74\u662fy\u8f74 \u2234\u5b83\u7684\u4e00\u6b21\u9879\u7cfb\u6570\u4e3a0 \u2234m=5
\u2234\uff08x\uff0cy\uff09\u4e3a\uff080 \uff0c2\uff09
\u8fd9\u4e2a\u51fd\u6570\u7684\u89e3\u6790\u5f0f\u4e3ay=-1/2x²+2
\u629b\u7269\u7ebfy=-2x²+6x-1\u7684\u9876\u70b9\u5750\u6807\u4e3a\uff1f\u5bf9\u79f0\u8f74\u4e3a\uff1f
\u89e3\uff1ay=-2(x²-3x)-1=-2[(x-3/2)²-9/4]-1=-2(x-3/2)²+9/2-1=-2(x-3/2)²+7/2
\u6545\u9876\u70b9\u5750\u6807\u4e3a(-3/2\uff0c7/2)\uff1b\u5bf9\u79f0\u8f74\uff1ax=3/2.
开口向上
对称轴x=3/2
顶点坐标(3/2,0.5)
解:y=2x²-6x+5=2(x²-3x)+5=2[(x-3/2)²-9/4]+5=2(x-3/2)²-9/2+5=2(x-3/2)²+1/2
开口朝上;对称轴x=3/2;顶点(3/2,1/2).
y=2x平方-6x+5=2(x-3/2)^2+1/2
开口方向向上
对称轴x=3/2
顶点坐标(3/2,1/2)
y=2(x-3/2)^2 + 1/2, 开口向上,对称轴:x=3/2,顶点坐标:(3/2,1/2)
y=2(x-2/3)平方+1/2
开口方向向上
对称轴 x=3/2
定点坐标 (3/2,1/2)
绛旓細浣犲ソ锛佸鍥惧厛姹傚嚭浜ょ偣锛岀敾鍑哄浘褰㈠尯鍩燂紝鍐嶇敤瀹氱Н鍒嗘眰鍑洪潰绉傜粡娴庢暟瀛﹀洟闃熷府浣犺В绛旓紝璇峰強鏃堕噰绾炽傝阿璋紒
绛旓細姹傚,鍏堟妸鎵姹備唬鏁板紡鍖栫畝,娑堝幓y,鐒跺悗褰掔粨鍒颁簩娆″嚱鏁版眰鏋佸.鐢2x^2-6x+y^2=0,寰,y^2=-2x^2+6x,锛1锛夌劧鍚庡皢锛1锛変唬鍏ユ墍姹.鍘熷紡锛漻^2-2ax2x^2+6x 锛-x^2+(6-2a)x 鍙湅鍋氭槸鍏充簬x鐨勪竴鍏冧簩娆″嚱鏁,鍐嶇‘瀹歺 鐨勫彇鍊艰寖鍥.鐢憋紙1锛夊紡,寰梱^2=-2x^2+6x>=0,瑙e嚭0 ...
绛旓細鍗y=-2x²+6x鈮0 鎵浠2x(x-3)鈮0 0鈮鈮3 鎵浠ュ師寮=x²+(-2x²+6x)+2x =-x²+8x =-(x-4)²+16 鎵浠=3 鏈澶у兼槸15
绛旓細鍥炵瓟锛氳В:璁句袱鏍瑰垎鍒负x1,x2 鏁呮湁x1+x2=-3 x1x2=m\2=2 鏁卪鐨勫间负4
绛旓細璇鎶涚墿绾瀵圭О杞翠负锛-b/2a=1.5 鎵浠ユ柊鎶涚墿绾垮绉拌酱涓猴細-1.5 鎵浠ワ細-b'/2*(-2)=-1.5 b=-6 鎵浠ユ柊鎶涚墿绾胯В鏋愬紡涓猴細y=-2x^2-6x
绛旓細鍏堥厤鏂 Y=2(X锛3/2)骞虫柟锛15/2 鎵浠ラ《鐐逛负(3/2,-15/2)瀵圭О杞翠负X=3/2
绛旓細鍜寈杞寸殑浜ょ偣鐨勬í鍧愭爣灏辨槸2x²+6x+c=0鐨勬牴 鎵浠1+x2=-3,x1x2=c/2 璺濈鏄2 |x1-x2|=2 (x1-x2)²=4 鎵浠(x1-x2)²=(x1+x2)²-4x1x2=4 9-2c=4 c=5/2
绛旓細y=2x2-6x+1鏄笉鑳界敱y=2x绉诲姩寰楀埌鐨勶紝鍥犱负涓涓槸鎶涚墿绾锛屼竴涓槸鐩寸嚎 y=2x^2-6x+1 y=2(x^2-3x+1/2)y=2(x^2-3x+9/4-9/4+1/2)y=2(x-3/2)^2-7/2 椤剁偣涓猴紙3/2,-7/2锛
绛旓細椤剁偣鍗(3锛-8)鑰屾洸鐜囩殑鍏紡涓簁=y''/[(1+(y')^2)^(3/2)]y=x²-6x+1锛屽嵆y'=2x-6锛寉''=2 寰楀埌k=2/[(1+(2x-6)^2)^(3/2)]浠e叆x=3锛屽嵆鏇茬巼涓2 閭d箞鏇茬巼鍗婂緞涓1/2
绛旓細鈭2x^2-6x+y^2=0 鈭磞^2=-2x^2+6x鈮0 鍗硏^2-3x鈮0 鈭0鈮鈮3 鈭磝^2+y^2+2x =x^2-2x^2+6x+2x =-x^2+8x =-(x-4)^2+16 鈭0鈮鈮3 鈭村綋x=0鏃讹紝鍘熷紡鍙栧緱鏈灏忓0 褰搙=3鏃讹紝鍘熷紡鍙栧緱鏈澶у15