SOLUTION: Write a word problem involving finding two real numbers that could be solved with the equation x(9-x)=14. Then Determine what the axis of symmetry and the maximum or minimum point

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write a word problem involving finding two real numbers that could be solved with the equation x(9-x)=14. Then Determine what the axis of symmetry and the maximum or minimum point      Log On


   

Question 1025085: Write a word problem involving finding two real numbers that could be solved with the equation x(9-x)=14.
Then Determine what the axis of symmetry and the maximum or minimum point of the graph of the
equation would be without graphing the equation. Solve by graphing and then solve in 2 other ways. Thanks!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A student went online and asked help for solving the equation x%289-x%29=14.
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9x-x%5E2=14
x%5E2-9x%2B14=0
x%5E2-9x%2B%289%2F2%29%5E2%2B14=%289%2F2%29%5E2
%28x-9%2F2%29%5E2=81%2F4-56%2F4
%28x-9%2F2%29%5E2=+25%2F4
Vertex is (9%2F2,25%2F4).
The axis of symmetry is x=9%2F2.
It's a minimum since the quadratic coefficient 1%3E0.
Completing the square,
x-9%2F2=0+%2B-+%285%2F2%29
x=9%2F2+%2B-+%285%2F2%29
x=14%2F2=7 and x=4%2F2=2
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You can also solve with the quadratic equation using a=1,b=-9,c=14
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
I'll leave that for you.
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