Question

What is the vertex form of `y= x^2+8x+20`?

Answer 1

Vertex is (-4,4 )

Explanation:

`y=x^2+8x+20`

this can also be written as ,
y = `x^2 + 8x + 4^2 - 4^2 + 20`

which can be further simplified into,
y = `(x+4)^2 + 4` ........ (1)

We know that,
`y = (x-h)^2 + k` where vertex is (h,k)

comparing both the equations we get vertex as (-4,4)

graph{x^2 + 8x +20 [-13.04, 6.96, -1.36, 8.64]}

Answer 2

`y=(x+4)^2 +4`

Explanation:

The vertex form is: `y=a(x-h)^2+k`

when `(h, k)` is dhe vertex of the parabola `ax^2+bx+c`

`h=-b/(2a)`, `k=-Delta/(4a)=-(b^2-4ac)/(4a)`.

Now: `y=x^2+8x+20rArrh=-8/2 =-4` and `k=-(64-4*1*20)/(4*1)=4`

then the vertex form is: `y=(x+4)^2 +4`

Second method:

`y=x^2+8x+20rArr y-20=x^2+8xrArr`

`y-20+16=x^2+8x +16rArr y-4=(x+4)^2rArr`

`y=(x+4)^2 +4`