Question

A rectangular picture measuring 3 in. by 8 in. is surrounded by a frame with uniform

width x. Complete the quadratic function below, in standard form, to show the
combined area of the picture and frame.
f(x) =

Answer 1

• f(x) = 4x² + 22x + 24

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The combined dimensions of the rectangle are:

• w = 3 + 2x and
• l = 8 + 2x,

since x is added to both ends.

The area of rectangle will be:

• A = lw

or

• f(x) = (3 + 2x)*(8 + 2x)
• f(x) = 3*8 + (3 + 8)(2x) + (2x)²
• f(x) = 24 + 22x + 4x²
• f(x) = 4x² + 22x + 24