Question

x^+8x+20 as a perfect square plus a constant then sketch the graph

Answer 1

I assume you meant x^2

(x^2+8x+16)+4
(x+4)^2+4

Answer 2

Some quadratics can be factored into two identical binomials. These quadratics are called perfect square trinomials. Perfect square trinomials can be factored as follows:

a^2+2ab+b^2=(a+b)^2

OR

a^2-2ab+b^2=(a-b)^2

In this case:

a=1

2ab=8

2*1*b=8

2b=8 Diwide both sides with 2

b=4

(x+4)^2=x^2+2*x*4+4^2

(x+4)^2=x^2+8x+16

x^+8x+20 = x^2+8x+16+4 = (x+4)^2+4

Graph:
In google type:
functions graphs online

When you see list of results click on:

rechneronline.de/function-graphs/

When page be open in blue rectangle type:
Range x-axis from

In displayproperties type:

Range x-axis from -10 to 10

Range y-axis from -1 to 19

and click option Draw

You also can calculate values of expresion:

x^+8x+20 = (x+4)^2+4


x= -10
(x+4)^2+4=(-10+4)^2+4=(-6)^2+4=36+4=40

x= -9
(x+4)^2+4=(-9+4)^2+4=(-5)^2+4=25+4=29

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

etc.

Answer 3

rechneronline.de/function-graphs/

IN BLUE RECTANGLE TYPE:


(x+4)^2+4