Respuesta :

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).

Therefore, the minimum of this function is at -2. Since the vertex is the lowest point of this parabola.

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