Question

Write g(x) = 40x + 4x2 in vertex form.

Answer 1

4x^2 + 40 x
= 4 (x^2 + 10x)
= 4 (x+ 5)^2 - 25)
= 4(x + 5)^2 - 100

Answer 2

`g(x) =4(x+5)^2-100`

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