Question

二次函数一般式a+2b和a-2b的值如何确定?还有a+b+c的值和4a-2b+c的值都如何确定?

Answer 1

二次函数f(x)=ax^2+bx+c

x=1时的函数值即为f(1)=a+b+c

x=-2时的函数值即为f(-2)=4a-2b+c

f(0)=c

f(1/2)=a/4+b/2+c

f(-1/2)=a/4-b/2+c

f(1/2)-f(0)=a/4+b/2,得：a+2b=4[f(1/2)-f(0)]

f(-1/2)-f(0)=a/4-b/2,得：a-2b=4[f(-1/2)-f(0)]