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a)

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Given function f(x) = x²+3x-7

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x2 + 3x - 7

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General Completed square form is a(x+d)2 + e

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To change the expression into a Completed square form add and suntract (half the x coefficient)²

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Here x coefficient = 3. so, (half the x coefficient)² = (3/2)2= 9/4.

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Add 9/4 to each side.

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x2 + 3x - 7 + 9/4 - 9/4

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x2 + 3x + 9/4 - 9/4 - 7

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x2 + 3x + (3/2)² - (28 + 9)/4

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(x + 3/2)2 - 37/4

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The Completed square form is (x + 3/2)2 - 37/4

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b)

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Given function f(x) = 10 - 4x - x²

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10 - 4x - x²

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10 - ( 4x + x² )

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General Completed square form is a(x+d)2 + e

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To change the expression into a Completed square form add and subtract (half the x coefficient)²

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Here x coefficient = 4. so, (half the x coefficient)² = (4/2)2 = 2² = 4.

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Add 2 to each side.

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10 - ( 4x + x² ) + 4 - 4

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10 + 4 - ( 4x + x² ) - 4

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10 + 4 - ( 4x + x² + 4 )

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10 + 4 - ( x² + 4x + 2² )

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14 - (x + 2)2

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The Completed square form is 14 - (x + 2)2

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