Question

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?

Answer 1

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}`