Question 1030562
): For each quadratic function, state the vertex and then graph the function
Julie wants to place 44 ft of picket fencing around a garden so as to create the largest rectangular area possible.
A.) If x represents the width, write an algebraic expression that represents the length
The perimeter of the garden is 44 ft, therefore:
2L + 2x = 44
simplify, divide by 2
L + x = 22
L = -x+22, represents the length
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B.) Write a function rule, f(x), that models the area of the garden
f(x) = x(-x+22)
f(x) = -x^2 + 22x
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C.) What is the maximum point on the parabola? (Only maximum would make sense)
the maximum point occurs on the axis of symmetry x = b/(2a)
x = {{{(-22)/(2*-1)}}}
x = 11 ft is the x value for the max point
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D.) Find the dimensions of the garden with the maximum area
L = -11 + 22
L = 11 ft, obviously, it is a square
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E.) What is the maximum area? 
11^2 = 121 sq/ft