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The greatest area corresponds to the vertex of the graph.
G
The maximum of the function f corresponds to the vertex of the graph.
Let's recall the formula.
Equation:f(x)= ax^2+ bx+ c
Axis of symmetry:x=-b/2 a
x-coordinate of the vertex:-b/2 a
Let's expand the given expression and identify the coefficients of the quadratic.
Distribute x
Identity Property of Addition
Commutative Property of Addition
We now have the quadratic in standard form with coefficients a= -2, b= 120, and c= 0. Let's use these coefficients to find the x-coordinate of the vertex.
To find the second coordinate of the vertex, we substitute x=30 in the equation.
The vertex corresponds to the maximum of the function. Since the function represents the area of the enclosure, this result means that the greatest area Adrian can enclose with the fencing is 1800 square feet. The correct answer is G.