Answer:
\(g(x) =4(x+5)^2-100\)
Step-by-step explanation:
\(g(x) = 40x + 4x^2\)
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
\(g(x) =4x^2+40x\)
\(g(x) =4(x^2+10x)\)
Coefficient of x is 10 , 10 divide by 2= 5
5^2= 25
Add and subtract 25
\(g(x) =4(x^2+10x+25-25)\)
\(g(x) =4(x^2+10x+25)-100\)
Now factor x^2 +10x+25, it becomes \((x+5)(x+5)\)
\(g(x) =4(x+5)(x+5)-100\)
\(g(x) =4(x+5)^2-100\) is our vertex form
