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a)\(x^2-4x+1\)

\(=\left(x^2-4x+4\right)-3\)

\(=\left(x-2\right)^2-3\ge-3\)

When \(x=2\)

b)\(3x^2-6x-1\)

\(=3x^2-6x+3-4\)

\(=3\left(x^2-2x+1\right)-4\)

\(=3\left(x-1\right)^2-4\ge-4\)

When \(x=1\)

c)\(4x^2+4x-2\)

\(=4x^2+4x+1-3\)

\(=\left(2x+1\right)^2-3\ge-3\)

When \(x=-\dfrac{1}{2}\)

Exercise 2:

a)\(4x-x^2-5\)

\(=-x^2+4x-4-1\)

\(=-\left(x^2-4x+4\right)-1\)

\(=-\left(x-2\right)^2-1\le-1\)

When \(x=2\)

b)\(5-x^2-6x\)

\(=-x^2-6x-9+14\)

\(=-\left(x^2+6x+9\right)+14\)

\(=-\left(x+3\right)^2+14\le14\)

When \(x=-3\)