Algebra

Completing The Square Generalized

Completing the Square - Higher Degree Polynomials

         

If the function y=(x22x)2+16x232xy=(x^2-2x)^2+16x^2-32x has the minimum value bb at x=ax=a, what is aba-b?

For x>0x>0, the function y=x4+18x274y=-x^4+18x^2-74 has a maximum value y=by=b at x=ax=a. What is a+ba+b?

What is the sum of the maximum and minimum values of y=(x22x+8)216(x22x+8)+84y=(x^2-2x+8)^2-16(x^2-2x+8)+84 in the domain 0x30 \leq x \leq 3?

For x>0x>0, the function y=x410x2+31y=x^4-10x^2+31 has a minimum value y=by=b at x=ax=\sqrt{a}. What is a+ba+b?

For x>0x>0, the function y=x4+8x24y=-x^4+8x^2-4 has a maximum value y=by=b at x=ax=a. What is a+ba+b?

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