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# Help with Math HW

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

Feb 26, 2019

#1
+23636
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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
+23636
0

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
+24978
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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

Feb 26, 2019