Unformatted text preview: king you to find. example: 40 m of wire fencing will be used to make a rectangular plot that encloses a play area for
your pet dog. A wall of your house is to serve as one side of the plot. What dimensions
would give a maximum plot area?
1) Define variables and write expressions.
• The area must be maximized.
• We need an area function that is quadratic. The area of a
rectangle is the product of its width and length. Write
expressions for the dimensions of the plot. house
plot Let A represent the plot's area in square metres.
Let x represent the length of the plot's side perpendicular to the house's wall in metres.
Then 40 − 2x represents the length of the plot's side parallel to the house's wall in metres.
2) Write the quadratic area function. 3) Solve the equation; write it in vertex form. A = x (40 − 2x)
A = 40x − 2x2
A = −2x2 + 40x
A = −2[x2 − 20x
A = −2[x − 20x + 100 − 100]
A = −2[(x − 10)2 − 100]
A = −2(x − 10)2 − 2(−100)
A = −2(x − 10)2 + 200
The vertex is (10,200) and...
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