已知抛物线y=ax2+x+2. (1)当a=-1时,求此抛物线的顶点坐标和对称轴; (2)若代数式-x2+x+2的值为正整数,求x的值; (3)当a=a1时,抛物线y=ax2+x+2与x轴的正半轴相交于点M(m,0);当a=a2时
已知抛物线y=ax2+x+2.
(1)当a=-1时,求此抛物线的顶点坐标和对称轴;
(2)若代数式-x2+x+2的值为正整数,求x的值;
(3)当a=a1时,抛物线y=ax2+x+2与x轴的正半轴相交于点M(m,0);当a=a2时,抛物线y=ax2+x+2与x轴的正半轴相交于点N(n,0).若点M在点N的左边,试比较a1与a2的大小.
(1)当a=-1时,求此抛物线的顶点坐标和对称轴;
(2)若代数式-x2+x+2的值为正整数,求x的值;
(3)当a=a1时,抛物线y=ax2+x+2与x轴的正半轴相交于点M(m,0);当a=a2时,抛物线y=ax2+x+2与x轴的正半轴相交于点N(n,0).若点M在点N的左边,试比较a1与a2的大小.
数学人气:792 ℃时间:2020-01-29 13:21:07
优质解答
(1)当a=-1时,y=-x2+x+2=-(x-12)2+94∴抛物线的顶点坐标为:(12,94),对称轴为x=12;(2)∵代数式-x2+x+2的值为正整数,-x2+x+2=-(x-12)2+214≤214,∴-x2+x+2=1,解得x=1±52,或-x2+x+2=2,解得x=0或1....
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