Rectangular implies the area to be length times height
let height=x
let width=2 more than the height or Length=2+x
Area=F(x)=(2+x)(x)=2x+x^2
f(x)=x^2+2x
****************To Answer your Additional question
You see the standard price is $100 for any mural, And also charges $40 per square foot.
So to show you the approach, Lets say that a mural of 1 square feet needs to be painted, then the charge will be $100 plus the $40 for every square feet, then it will be 100+40(1 square feet)=$140.
The problem asks for the charge of mural whose area is x, so lets do the same thing.
$100+40(x square feet)=100+40x and that is the function that gives the price of mural with an area of x.
so, g(x)=100+40x
the discriminant b^2 - 4ac when the equation is in the form of ax^2 +bx+c=0
13x^2-16x = x^2 -x
we need to get in it the standard form
subtract x^2 from each side
12x^2 -16x = -x
add x to each side
12x^2 -15x = 0
12x^2 -15x -0 =0
a=12 b=-15 c=0
b^2 -4ac
the discriminant = b^2
b^2 = (-15)2 = 225
The answer is 0 because if you substitute x with 1 and solve the equation you get 0
