the area of a square is 4x^2+12x+9. Write an expression to represent the length of the side of the square.

An expression to represent the length of the side of the square with an area of 4x^2+12x+9 in terms of x is 2x + 3

Step-by-step explanation:

all sides of a square are equal in length.

area of a square is the side length squared.

area a, side s, variable x.

a = 4x^2 + 12x + 9.   s = ?   x = ?

a = s^2.

a = 4x^2 + 12x + 9.

4x^2 + 12x + 9 = s^2.

x^2 + 3x + 9/4 = (s^2)/4.

factor x^2 + 3x + 9/4 = (s^2)/4.

(x + 3/2)(x + 3/2) = (s^2)/4.

(x + 3/2)^2 = (s^2)/4.

√((x + 3/2)^2) = √((s^2)/4).

take positive root.

x + 3/2 = s/2

solve for side s.

s/2 = x + 3/2

s = 2x + 3

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.