I assume you meant x^2
(x^2+8x+16)+4
(x+4)^2+4
x^+8x+20 as a perfect square plus a constant then sketch the graph
3 answers
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.
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.
rechneronline.de/function-graphs/
IN BLUE RECTANGLE TYPE:
(x+4)^2+4
IN BLUE RECTANGLE TYPE:
(x+4)^2+4