Respuesta :

Answer:

So, the vertex form of your function is  [tex]y(x)=2*(x+2)^2-7[/tex].

The vertex is at [tex](-2|-7)[/tex]

Step-by-step explanation:

Given function:

[tex]y(x)=2*x^2+8x+1[/tex]

Steps:

[tex]y(x)=2*x^2+8x+1\\[/tex]

[tex]y(x)=2(x^2+4x+\frac{1}{2} )[/tex]    (Factor out)

[tex]y(x)=2(x^2+4x+2^2-2^2+\frac{1}{2} )[/tex]  (Complete the square)

[tex]y(x)=2((x+2)^2-2^2+\frac{1}{2} )[/tex]  (Use the binomial formula)

[tex]y(x)=2((x+2)^2-\frac{7}{2} )[/tex]  (Simplify)

[tex]y(x)=2*(x+2)^2-7[/tex] (Expand)
y = a ( x − h ) 2 + k is vertex form.

-b/2a to get x of vertex (x , y)

-8/4 = -2

So far we have (-2, y)

plug -2 into equation:

y = 2(-2)^2 - 16 + 1

y = -7

(-2, -7)

so 2(x+2)^2 - 7