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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?

Sagot :

Given:

[tex]y=x^2+4x+7[/tex]

Find: the manimum value of the function.

Explanation:

[tex]\begin{gathered} y=x^2+4x+7 \\ y^{^{\prime}}=2x+4 \\ y^{^{\prime}}=0 \\ 2x+4=0 \\ x=-2 \end{gathered}[/tex]

ar x=-2,

the function will be

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

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