二次函數(shù)f(x)=ax^2+bx+c,若函數(shù)y=f(x+1)是偶函數(shù),則a/b=請(qǐng)注明過程,謝謝!

熱心網(wǎng)友

f(x+1)=a(x+1)^2+b(x+1)+cf(-x+1)=a(-x+1)^2+b(-x+1)+c因?yàn)閒(x+1)是偶函數(shù)所以f(x+1)=f(-x+1)化簡得：4ax=-2bx對(duì)任意x都成立所以a/b=-1/2其實(shí)由二次函數(shù)的圖像看可輕易看出f(x)的對(duì)稱軸是x=1可得答案

熱心網(wǎng)友

f(x+1)是偶函數(shù)證明x=-1是二次函數(shù)的對(duì)稱軸啊