4) Edgar builds a sand castle with a rectangular base. The side lengths of the base are 25 in, and 16 in. He wants to surround the castle's base with a moat that is w inches wide. Write a quadratic function, A, in standard form to
represent the combined area taken up by the castle and the moat.
16in.
25 in.

4w² + 82w + 400

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients involving addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A quadratic function is a polynomial of degree 2. The standard form of a quadratic equation is:

ax² + bx + c

The moat has width of w inch. Therefore:

combined width of castle and moat = 16 in + w in + w in = 16 + 2w in

combined length of castle and moat = 25 in + w in + w in = 25 + 2w in

The combined area = length * width = (16 + 2w)(25 + 2w) = 400 + 32w + 50w + 4w² = 4w² + 82w + 400

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step-by-step explanation:

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