已知抛物线y=x²+mx-3/4m²(m>0)与x轴交于A、B两点 (1)求证:抛物线的对称轴在y轴的左侧;(2)若1/OB-1/OA=2/3(O是坐标原点),求抛物线的解析式;(3)设抛物线与y轴的交于点C,若
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![已知抛物线y=x²+mx-3/4m²(m>0)与x轴交于A、B两点 (1)求证:抛物线的对称轴在y轴的左侧;(2)若1/OB-1/OA=2/3(O是坐标原点),求抛物线的解析式;(3)设抛物线与y轴的交于点C,若](/uploads/image/z/6969397-13-7.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dx%26%23178%3B%2Bmx-3%2F4m%26%23178%3B%EF%BC%88m%3E0%EF%BC%89%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%BA%8EA%E3%80%81B%E4%B8%A4%E7%82%B9+%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E5%9C%A8y%E8%BD%B4%E7%9A%84%E5%B7%A6%E4%BE%A7%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A51%EF%BC%8FOB%EF%BC%8D1%EF%BC%8FOA%3D2%EF%BC%8F3%28O%E6%98%AF%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%29%2C%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%9B%EF%BC%883%EF%BC%89%E8%AE%BE%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8Ey%E8%BD%B4%E7%9A%84%E4%BA%A4%E4%BA%8E%E7%82%B9C%2C%E8%8B%A5)
已知抛物线y=x²+mx-3/4m²(m>0)与x轴交于A、B两点 (1)求证:抛物线的对称轴在y轴的左侧;(2)若1/OB-1/OA=2/3(O是坐标原点),求抛物线的解析式;(3)设抛物线与y轴的交于点C,若
已知抛物线y=x²+mx-3/4m²(m>0)与x轴交于A、B两点 (1)求证:抛物线的对称轴在y轴的左侧;
(2)若1/OB-1/OA=2/3(O是坐标原点),求抛物线的解析式;
(3)设抛物线与y轴的交于点C,若△ABC是直角三角形,求△ABC的面积
已知抛物线y=x²+mx-3/4m²(m>0)与x轴交于A、B两点 (1)求证:抛物线的对称轴在y轴的左侧;(2)若1/OB-1/OA=2/3(O是坐标原点),求抛物线的解析式;(3)设抛物线与y轴的交于点C,若
(1).证明:由于y=x²+mx-3/4m²=(x+m/2)²-m²/4-3m²/4=(x+m/2)²-m²;
该抛物线对称轴为x=-m/2; m>0; 故该抛物线的对称轴在y轴的左侧;
(2).x²+mx-3/4m²=(x+m/2)²-m²=(x+m/2+m)(x+m/2-m)=(x+3m/2)(x-m/2)=0;
x1=-3m/2; x2=m/2; 由于1/OB-1/OA=2/3;故1/OB>1/OA; OA>OB; 所以:A(-3m/2,0);
B(m/2,0); OB=m/2; OA=3m/2; 1/OB-1/OA=2/m-2/(3m)=2/3;
6-2=2m=4; m=2; 故该抛物线解析式为:y=x²+2x-3;
(3).令x=0,则y=-3m²/4; 故 C(0,-3m²/4); 由(2)知:A(-3m/2,0); B(m/2,0);
AC²=9m²/4+9m^4/16; BC²=m²/4+9m^4/16; AB²=(m/2+3m/2)²=4m²;
当AC²+BC²=AB²时 ;5m²/2+9m^4/8=4m²; 5/2+9m²/8=4; 20+9m²=32; m²=12/9;
m=2√3/3;
当AC²=BC²+AB²时,9m²/4+9m^4/16=m²/4+9m^4/16+4m²;2m²=4m²; m=0; 这是不可能的;
故:m=2√3/3;m²=4/3; AB²=16/3; AC²=4; BC²=4/3; ;
AB=4/√3; AC=2; BC=2/√3; C为直角; △ABC的面积=AC×BC/2=2/√3=2√3/3;