已知函数f(x)=x^2+bx+c(b,c∈R),(1)若f(1)=0,f(3)=0,求f(-1)的值;(2)若函数f(x)在[-2,+∞)上是单调增函数,且c=-b^2,求f(2)的取值范围;(3)若对任意x∈R,恒有f(x)≥2x+b,证明:当x≥0时,f(x)≤(x+c)^2.
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![已知函数f(x)=x^2+bx+c(b,c∈R),(1)若f(1)=0,f(3)=0,求f(-1)的值;(2)若函数f(x)在[-2,+∞)上是单调增函数,且c=-b^2,求f(2)的取值范围;(3)若对任意x∈R,恒有f(x)≥2x+b,证明:当x≥0时,f(x)≤(x+c)^2.](/uploads/image/z/1980105-33-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E2%2Bbx%2Bc%28b%2Cc%E2%88%88R%29%2C%281%29%E8%8B%A5f%281%29%3D0%2Cf%283%29%3D0%2C%E6%B1%82f%28-1%29%E7%9A%84%E5%80%BC%EF%BC%9B%282%29%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%5B-2%2C%2B%E2%88%9E%29%E4%B8%8A%E6%98%AF%E5%8D%95%E8%B0%83%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E4%B8%94c%3D-b%5E2%2C%E6%B1%82f%282%29%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%EF%BC%9B%283%29%E8%8B%A5%E5%AF%B9%E4%BB%BB%E6%84%8Fx%E2%88%88R%2C%E6%81%92%E6%9C%89f%28x%29%E2%89%A52x%2Bb%2C%E8%AF%81%E6%98%8E%EF%BC%9A%E5%BD%93x%E2%89%A50%E6%97%B6%2Cf%28x%29%E2%89%A4%EF%BC%88x%2Bc%29%5E2.)
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