Question

Felix surrounds a 12 in. by 8 in. photo with a frame that is x inches wide. Which quadratic function represents the combined area A of the picture and the frame?

A. A(x) = x^2 + 20x + 96

B. A(x) = x^2 + 40x + 96

C. A(x) = 4x^2 + 20x + 96

D. A(x) = 4x^2 + 40x + 96

Answer 1

D: A(x) = 4x² + 40x + 96

Explanation:

Dimensions of photo is;

Length; L = 12 inches

Width; W = 8 inches

Now, this picture is surrounded by a frame that is "x" inches wide. Thus, new dimensions are;

L_new = 12 + x + x = 2x + 12

W_new = 8 + x + x = 2x + 8

New area is;

A_new = (2x + 12) × (2x + 8)

A_new = 4x² + 24x + 16x + 96

A_new = 4x² + 40x + 96