The given function is
[tex]f(x)=2x^2+16x+30[/tex]To find the minimum of this function, we have to find the vertex of the parabola V(h,k). Where
[tex]h=-\frac{b}{2a},k=f(h)[/tex]Where a = 2, and b = 16. Replacing these values, we have
[tex]h=\frac{-16}{2(2)}=-\frac{16}{4}=-4[/tex]Then, we find k
[tex]k=f(-4)=2(-4)^2+16(-4)+30=2(16)-64+30=-2[/tex]So, the vertex is at (-4, -2).
