Answer:
The vertex form of a quadratic function is given by [tex]y = a(x - h)^2 + k[/tex] , where (h, k) is the vertex of the parabola.
Given the function :
g(x) = [tex]4x^2+88x[/tex]
g(x) = [tex]4(x^2+22x)[/tex]
Now, we will be completing the square ;
g(x) = [tex]4(x^2+22x+11^2-11^2)[/tex] = [tex]4(x^2+88x+11^2)-4 \cdot(11^2)[/tex]
⇒ g(x) =[tex]4 (x+11)^2 -4 \cdot 121[/tex] or
[tex]g(x) =4(x+11)^2 - 484[/tex]
therefore, the given function is in the vertex form is, [tex]g(x) =4(x+11)^2 +(-484)[/tex]
