问题
填空题
将抛物线y=2x2-12x+10绕它的顶点旋转180°,所得抛物线的解析式是______.
答案
y=2x2-12x+10,
=2(x2-6x)+10,
=2(x2-6x+9-9)+10,
=2(x2-6x+9)-18+10,
=2(x-3)2-8,
将原抛物线绕顶点旋转180°后,得y=-2(x-3)2-8,
即:y=-2x2+12x-26,
故答案为:y=-2x2+12x-26.
将抛物线y=2x2-12x+10绕它的顶点旋转180°,所得抛物线的解析式是______.
y=2x2-12x+10,
=2(x2-6x)+10,
=2(x2-6x+9-9)+10,
=2(x2-6x+9)-18+10,
=2(x-3)2-8,
将原抛物线绕顶点旋转180°后,得y=-2(x-3)2-8,
即:y=-2x2+12x-26,
故答案为:y=-2x2+12x-26.