Why put x = 1 , x = − 1 , x = 0 here?ProblemAssume f ( x ) = a x 2 + b x + c and | f ( x ) | ≤ 1 ( x ∈ [ − 1 , 1 ] ) Prove | c x 2 − b x + a | ≤ 2 ( x ∈ [ − 1 , 1 ] ) .

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Why put   x  =  1  ,  x  =  −  1  ,  x  =  0 here?ProblemAssume   f  (  x  )  =  a      x    2    +  b  x  +  c and       |    f  (  x  )      |    ≤  1  (  x  ∈  [  −  1  ,  1  ]  ) Prove       |    c      x    2    −  b  x  +  a      |    ≤  2  (  x  ∈  [  −  1  ,  1  ]  ) .

mar1nerne · Accepted Answer

Step 1You can use any three points you want. You will get a set of three equations in the three unknowns a, b, c. Using   ±  1  ,  0 makes the equations very simple because 0 isolates c and   ±  1 are easy to square and the opposite signs give the nice   a  +  b and   a  −  b .

Why put x = 1 , x = − 1 , x = 0 here? Problem Assume

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