1.设二次函数f(x)满足f(x+2)=f(2-x)且f(x)=0的两实数根平方和为10.图像过点(0,3).求f(x)的解析式.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 07:56:52
![1.设二次函数f(x)满足f(x+2)=f(2-x)且f(x)=0的两实数根平方和为10.图像过点(0,3).求f(x)的解析式.](/uploads/image/z/226943-71-3.jpg?t=1.%E8%AE%BE%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3f%28x%2B2%29%3Df%282-x%29%E4%B8%94f%28x%29%3D0%E7%9A%84%E4%B8%A4%E5%AE%9E%E6%95%B0%E6%A0%B9%E5%B9%B3%E6%96%B9%E5%92%8C%E4%B8%BA10.%E5%9B%BE%E5%83%8F%E8%BF%87%E7%82%B9%280%2C3%29.%E6%B1%82f%28x%29%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F.)
1.设二次函数f(x)满足f(x+2)=f(2-x)且f(x)=0的两实数根平方和为10.图像过点(0,3).求f(x)的解析式.
1.设二次函数f(x)满足f(x+2)=f(2-x)且f(x)=0的两实数根平方和为10.图像过点(0,3).求f(x)的解析式.
1.设二次函数f(x)满足f(x+2)=f(2-x)且f(x)=0的两实数根平方和为10.图像过点(0,3).求f(x)的解析式.
F(x)=ax^2+bx+c
①F(x+2)=f(2-x)
→ a(x+2)^2+b(x+2)+c=a(2-x)^2+b(2-x)+c
→ 8a+2b=0
→ b=-4a;
②图象过点(0,3),
→ F(0)=3 → c=3;
③ax^2-4ax+3=0的解x1、x2,满足(x1)^2+(x2)^2=10
→ (x1+x2)^2-2*x1*x2=10
→ (4a/a)^2-2*(3/a)=10
→ a=1.
F(x)=x^2-4x+3.