已知二次函數(shù)y=ax2+bx+c的圖象經(jīng)過A(-1,-5/2)B(0,-4) C(4,0)三點(diǎn),則二次函數(shù)的解析式是頂點(diǎn)D 的坐標(biāo)是 對(duì)稱軸方程是 S四邊形OBDC=
解析：∵二次函數(shù)y=ax2+bx+c的圖象經(jīng)過A(-1,-5/2)B(0,-4) C(4,0)三點(diǎn)
∴f(-1)=a-b+c=5/2
f(0)=c=-4
f(4)=16a+4b+c=0
聯(lián)立解得a=3/2,b=-5,c=-4
∴f(x)=3/2x^2-5x-4,對(duì)稱軸x=-b/(2a)=5/3,最小值-49/6
頂點(diǎn)D(5/3,-49/6)
過D作DE⊥X軸于E
∴E(5/3,0)
S(OBDC)=S(OEDB)+S(EDC)
梯形S(OEDB)=(4+49/6)*(5/3)/2=365/36
三角形S(EDC)=1/2*49/6*(4-5/3)=363/36
∴S(OBDC)=728/36好像不是y=3/2x^2-5x-4把(-1,-5/2) 帶進(jìn)去不符已知二次函數(shù)y=ax2+bx+c的圖象經(jīng)過A(-1,-5/2)B(0,-4) C(4,0)三點(diǎn)，則二次函數(shù)的解析式是頂點(diǎn)D 的坐標(biāo)是對(duì)稱軸方程是 S四邊形OBDC=解析：∵二次函數(shù)y=ax2+bx+c的圖象經(jīng)過A(-1,-5/2)B(0,-4) C(4,0)三點(diǎn)∴f(-1)=a-b+c=-5/2f(0)=c=-4f(4)=16a+4b+c=0聯(lián)立解得a=1/2，b=-1，c=-4∴f(x)=1/2x^2-x-4，對(duì)稱軸x=-b/(2a)=1，最小值-9/2頂點(diǎn)D(1,-9/2)過D作DE⊥X軸于E∴E(5/3,0)S(OBDC)=S(OEDB)+S(EDC)梯形S(OEDB)=(4+9/2)*(1)/2=17/4三角形S(EDC)=1/2*9/2*(4-1)=27/4∴S(OBDC)=11