Answer:
The y-value of the vertex is [tex]-12[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]f(x)=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
In this problem we have
[tex]f(x)=4x^{2}+8x-8[/tex] -----> this a vertical parabola open upward
Convert to vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)+8=4x^{2}+8x[/tex]
Factor the leading coefficient
[tex]f(x)+8=4(x^{2}+2x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)+8+4=4(x^{2}+2x+1)[/tex]
[tex]f(x)+12=4(x^{2}+2x+1)[/tex]
Rewrite as perfect squares
[tex]f(x)+12=4(x+1)^{2}[/tex]
[tex]f(x)=4(x+1)^{2}-12[/tex]
The vertex is the point [tex](-1,-12)[/tex]
The y-value of the vertex is [tex]-12[/tex]
