x^+8x+20 as a perfect square plus a constant then sketch the graph
I assume you meant x^2
(x^2+8x+16)+4
(x+4)^2+4
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.
rechneronline.de/function-graphs/
IN BLUE RECTANGLE TYPE:
(x+4)^2+4
To determine if the expression x^2 + 8x + 20 can be written as a perfect square plus a constant, we need to complete the square. Here's how you can do it:
Step 1: Take half of the coefficient of the x-term (which is 8 in this case) and square it: (8/2)^2 = 16.
Step 2: Add the value obtained in the previous step (16) to the expression.
x^2 + 8x + 16 + 4
Now, the expression can be rewritten as a perfect square plus a constant. In this case, it becomes:
(x + 4)^2 + 4
To sketch the graph, we can use this information. Since the expression is in the form (x + a)^2 + b, where a is the x-coordinate of the vertex and b is the y-coordinate, we can determine that the vertex of the graph is at (-4, 4).
Additionally, since the coefficient of the x^2 term is positive, the parabola opens upwards. The vertex represents the minimum point of the parabola.
To sketch the graph, start by plotting the vertex at (-4, 4). Then, plot a few more points to the left and right of the vertex by substituting different values of x into the equation. Finally, join these points smoothly to form the parabolic shape of the graph.
I hope this helps!