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

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Answer 1 · 2018-03-11T01:20:51

Vertex is (-4,4 )

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

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 · 2018-03-11T01:31:54

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

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:

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

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

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

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