Answer:
[tex]g(x) =4(x+5)^2-100[/tex]
Step-by-step explanation:
[tex]g(x) = 40x + 4x^2[/tex]
To get vertex form of equation y =a(x-h)^2+k
we use completing the square method
In completing the square method we take coefficient of x ,divide by 2 and then we square it
To apply completing the square method, we make x^2 alone
[tex]g(x) =4x^2+40x[/tex]
[tex]g(x) =4(x^2+10x)[/tex]
Coefficient of x is 10 , 10 divide by 2= 5
5^2= 25
Add and subtract 25
[tex]g(x) =4(x^2+10x+25-25)[/tex]
[tex]g(x) =4(x^2+10x+25)-100[/tex]
Now factor x^2 +10x+25, it becomes [tex](x+5)(x+5)[/tex]
[tex]g(x) =4(x+5)(x+5)-100[/tex]
[tex]g(x) =4(x+5)^2-100[/tex] is our vertex form
