Given the equation of the function:
[tex]f(x)=x^2+4x-7[/tex]
The given function represents a parabola
We will make a complete square to find the coordinates of the vertex
The coefficient of x = 4
Half the coefficient of x = 2
Square it give = 4
So, we will add and subtract 4
[tex]\begin{gathered} f(x)=x^2+4x+4-4-7 \\ f(x)=(x^2+4x+4)-11 \\ f(x)=(x+2)^2-11 \end{gathered}[/tex]
Compare the last equation with the vertex form of the parabola
[tex]f(x)=(x-h)^2+k[/tex]
So, h = -2, k = -11
So, the answer will be the coordinates of the vertex = (-2, -11)
