1.\x05已知二次函数y=f (x)=ax平方+bx=c 满足:|x|≤1时,|f(x)|≤1,求证:|x|≤1时,|2a+b|≤4.2.\x05若二次函数y=f(x)的图像过原点,且1≤f(-1) ≤2,3≤f(1) ≤4,求f(2)的取值范围.
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![1.\x05已知二次函数y=f (x)=ax平方+bx=c 满足:|x|≤1时,|f(x)|≤1,求证:|x|≤1时,|2a+b|≤4.2.\x05若二次函数y=f(x)的图像过原点,且1≤f(-1) ≤2,3≤f(1) ≤4,求f(2)的取值范围.](/uploads/image/z/5492483-35-3.jpg?t=1.%5Cx05%E5%B7%B2%E7%9F%A5%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0y%3Df+%28x%29%3Dax%E5%B9%B3%E6%96%B9%2Bbx%3Dc+%E6%BB%A1%E8%B6%B3%EF%BC%9A%7Cx%7C%E2%89%A41%E6%97%B6%2C%7Cf%28x%29%7C%E2%89%A41%2C%E6%B1%82%E8%AF%81%EF%BC%9A%7Cx%7C%E2%89%A41%E6%97%B6%2C%7C2a%2Bb%7C%E2%89%A44.2.%5Cx05%E8%8B%A5%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E8%BF%87%E5%8E%9F%E7%82%B9%2C%E4%B8%941%E2%89%A4f%28-1%29+%E2%89%A42%2C3%E2%89%A4f%281%29+%E2%89%A44%2C%E6%B1%82f%282%29%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
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1.\x05已知二次函数y=f (x)=ax平方+bx=c 满足:|x|≤1时,|f(x)|≤1,求证:|x|≤1时,|2a+b|≤4.2.\x05若二次函数y=f(x)的图像过原点,且1≤f(-1) ≤2,3≤f(1) ≤4,求f(2)的取值范围.
1.\x05已知二次函数y=f (x)=ax平方+bx=c 满足:|x|≤1时,|f(x)|≤1,求证:|x|≤1时,|2a+b|≤4.
2.\x05若二次函数y=f(x)的图像过原点,且1≤f(-1) ≤2,3≤f(1) ≤4,求f(2)的取值范围.
1.\x05已知二次函数y=f (x)=ax平方+bx=c 满足:|x|≤1时,|f(x)|≤1,求证:|x|≤1时,|2a+b|≤4.2.\x05若二次函数y=f(x)的图像过原点,且1≤f(-1) ≤2,3≤f(1) ≤4,求f(2)的取值范围.
1.因为:|x|≤1时,|f(x)|≤1
所以y=|f (0)|=|ax^2+bx+c|=|c|≤1
y=|f (1)|=|ax^2+bx+c|=|a+b+c|≤1
y=|f (-1)|=|ax^2+bx+c|=|a-b+c|≤1
所以|x|≤1时,|2a+b|≤4.
2.假设二次函数y=f (x)=ax^2+bx+c
所以f (0)=c=0
1≤f(-1) =a-b≤2,
3≤f(1)= a+b≤4
设s=f(2)=4a+2b,
此题转化为线性规划问题,
由图像即可求得.
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