SOLUTION: The sum of two numbers is 20. If one number is x, then the other number is ____. Their product is p(x)= _____. Find the maximum value of p. Write a quadratic function to solve.

Algebra ->  Functions -> SOLUTION: The sum of two numbers is 20. If one number is x, then the other number is ____. Their product is p(x)= _____. Find the maximum value of p. Write a quadratic function to solve.      Log On


   

Question 182249This question is from textbook algebra and trigonometry
: The sum of two numbers is 20. If one number is x, then the other number is ____. Their product is p(x)= _____. Find the maximum value of p. Write a quadratic function to solve. This question is from textbook algebra and trigonometry

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The sum of two numbers is 20. If one number is x, then the other number is ____.
It's quite obvious the other number = (20-x)
;
Their product is p(x)= _____.
p(x) = x(20-x)
p(x) = -x^2 + 20x
:
:
Find the maximum value of p.
Find the axis of symmetry using the formula x = -b/(2a)
x = %28-20%29%2F%282%2A-1%29
x = %28-20%29%2F%28-2%29
x = +10
:
Find max p(x), substitute 10 for x in the equation
p(x) = -(10^2) + 20(10)
p(x) = -100 + 200
p(x) = +100
:
:
Write a quadratic function to solve.
-x^2 + 20x = 0
Factor out -x
-x(x - 20) = 0
therefore:
x = 0
and
x = +20