Question

a designer is making a banner, as shown in the diagram, of width 3x and height 2x, where x is in feet. one foot of material on each side is gray, as shown below

Answer 1

a) f(x) = 6x^2 - 4x

b) 80 ft²

Explanation:

Refer to attached for full question

a.

Area formula for rectangle:

• A = wh

We see the width of the white part of the banner is 3x - 2 and height is 2x

Function to define the area

• f(x) = (3x - 2)*2x = 6x^2 - 4x

b.

If maximum width of white area is 10 ft, then the dimensions are:

• 3x - 2 = 10 ⇒ 3x = 12 ⇒ x = 4
• w = 10, h = 2*4 = 8
• A= 10*8 = 80 ft²