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If x is an integer, what is the smallest value of the expression x^2 - 6x +13?

Guest Feb 26, 2019

#1**+2 **

This is an upward opening parabola (like a bowl.) because the x^2 coefficient is positive

The minimum will occur at x = -b/2a

- (-6)/2 = 3 use this value to find f(x) 3^2 - 6(3) + 13 = 9-18+13 = 4 is the minimum value of the expression

ElectricPavlov Feb 26, 2019

#1**+2 **

Best Answer

This is an upward opening parabola (like a bowl.) because the x^2 coefficient is positive

The minimum will occur at x = -b/2a

- (-6)/2 = 3 use this value to find f(x) 3^2 - 6(3) + 13 = 9-18+13 = 4 is the minimum value of the expression

ElectricPavlov Feb 26, 2019

#2**+1 **

**If x is an integer, what is the smallest value of the expression x^2 - 6x +13?**

\(\begin{array}{|lrcll|} \hline & y &=& x^2 - 6x +13 \\ & &=& (x-3)^2 -9+13 \\ & &=& (x-3)^2 + 4 \qquad \text{min. if } x = 3 \\ & y &=& 0 + 4 \\ & y &=& 4 \\ \hline \end{array}\)

The smallest value of the expression \(x^2 - 6x +13\) is **4**

heureka Feb 26, 2019