SOLUTION: I don't know what number to use for width? "The function A(x)=x(10-x) describes the area A of a rectangular flower garden where x is it's width in yards. What is the maximum are

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Question 812154: I don't know what number to use for width?
"The function A(x)=x(10-x) describes the area A of a rectangular flower garden where x is it's width in yards. What is the maximum area of the garden?"
Please help. Thanks.
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
A(x) = x(10 - x)
10x - x^2
(-1)x^2 + 10x + 0 = Area
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the above quadratic equation is in standard form, with a=-1, b=10, and c=0
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the x coordinate of the max (or min) of the quadratic function is given by: x = -b/2a
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x = -b/2a
x = -10/2(-1)
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x = 5
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the y coordinate of the max (or min) of the quadratic function is found by evaluating the function at the x coordinate of the max (or min)
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y = (-1)x^2 + 10x + 0
y = (-1)5^2 + 10(5) + 0
y = -25 + 50 + 0
y = 25
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because a < 0 the vertex of the quadratic is a maximum, and (5, 25) is the maximum.
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Answer:
the maximum area of the garden is 25 sq.yd
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