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

 Feb 26, 2019

Best Answer 

 #1
avatar+18360 
+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

 Feb 26, 2019
 #1
avatar+18360 
+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
avatar+22188 
+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

 

laugh

 Feb 26, 2019

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