SOLUTION: Please help me to solve this problem. The daily profit for the garden department of a store from the sale of trees is given by P(x) = -x^2 + 18x + 144 , where x is the number of tr
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-> SOLUTION: Please help me to solve this problem. The daily profit for the garden department of a store from the sale of trees is given by P(x) = -x^2 + 18x + 144 , where x is the number of tr
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Question 461948: Please help me to solve this problem. The daily profit for the garden department of a store from the sale of trees is given by P(x) = -x^2 + 18x + 144 , where x is the number of trees sold. find the function's vertex and intercepts, and graph of the function. Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Please help me to solve this problem. The daily profit for the garden department of a store from the sale of trees is given by P(x) = -x^2 + 18x + 144 , where x is the number of trees sold. find the function's vertex and intercepts, and graph of the function.
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P(x) = -x^2 + 18x + 144
This is a 2nd degree equation so it is a parabola and it opens downward because of the negative coefficient of the leading term. Its standard form: y=(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
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y = -x^2 + 18x + 144
completing the square
y=-(x^2-18x+81)=144+81
y=-(x-9)^2+225
vertex: (9,225)
y-int
x=0
y=144
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x-int
y=0=-x^2 + 18x + 144
x^2-18x-144=0
(x-24)(x+6)=0
x=24
or
x=-6 (reject, x>0)
The maximum daily profit of 225 is achieved when 9 trees are sold
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See graph below
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