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Completing the square can be use to find the minimum value of the function represented by the equation y=x^2+4x+7. Where is the minimum value of the function located?

User BHS
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Given:


y=x^2+4x+7

Find: the manimum value of the function.

Explanation:


\begin{gathered} y=x^2+4x+7 \\ y^{^(\prime)}=2x+4 \\ y^{^(\prime)}=0 \\ 2x+4=0 \\ x=-2 \end{gathered}

ar x=-2,

the function will be


\begin{gathered} y=x^2+4x+7 \\ y(-2)=(-2)^2+4(-2)+7 \\ =4-8+7 \\ =11-8 \\ =3 \end{gathered}

User Troels Blum
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