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Completing The Square

This is completing the square on 'roids.

Higher Degree Polynomials

If the function \[y=(x^2-2x)^2+16x^2-32x\] has the minimum value \(b\) at \(x=a\), what is \(a-b\)?

For \(x>0\), the function \(y=-x^4+18x^2-74\) has a maximum value \(y=b\) at \(x=a\). What is \(a+b\)?

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

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

For \(x>0\), the function \(y=-x^4+8x^2-4\) has a maximum value \(y=b\) at \(x=a\). What is \(a+b\)?

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