Express x^2 - 8x + 17 in the form (x-p)^2 + q, where p and q are integers and find the minimum value of x^2 - 8x + 17.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The minimum value of x^2 - 8x + 17 has to be determined by the completion of squares.

x^2 - 8x + 17

=> x^2 - 8x + 16 + 1

=> (x - 4)^2 + 1

The term (x - 4)^2 is always >= 0. The minimum value of x^2 - 8x + 17 is when x - 4 = 0 or 1.

The expression takes the minimum value when x - 4 = 0 or x = 4.

x^2 - 8x + 17 takes the minimum value 1 when x = 4

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