抛物线y=ax2-2ax-3a(a

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抛物线y=ax2-2ax-3a(a
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抛物线y=ax2-2ax-3a(a
抛物线y=ax2-2ax-3a(a

抛物线y=ax2-2ax-3a(a
(1)y=ax²-2ax-3a=|a|*(-x²+2x+3)=|a|*(x+1)(-x+3),所以坐标 A(-1,0)、B(3,0);
(2)令 x=0,在 y=-3a,故坐标 C(0,-3a);
由 |OC|=|OB|=3,得:-3a=3,∴ a=-1;
抛物线的解析式为 y=-x²+2x+3;
(3)设坐标 P(x,3-x²+2x),连 OP,则:
S=S△pob+S△poc-S△boc=|OB|*y/2+|OC|*x/2-|OB|*|OC|/2
=3(3-x²+2x)/2+(3x/2)-3*3/2=(3/2)(3x-x²);
当 x=(x1+x2)/2=(0+3)/2=3/2 时,max{S}=(3/2)*(3/2)²=27/8;