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Production is profitable only when revenue is greater than cost.
The monthly profit of a company selling 
x units is given by the quadratic function:

P(x)=-(1)/(200)x^(2)+30 x
Which of the following equivalent expressions displays the break-even point as a constant or coefficient?
Choose 1 answer:
(A) 
-(1)/(200)((x-3,000)^(2)-9,000,000)
(B) 
-(1)/(2.00)(x-3,000)^(2)+45,000
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Khan Academy Donate ^{(33)} embongw s blazing! 22 week streak Level 1515 111111//111111 skills Production is profitable only when revenue is greater than cost. The monthly profit of a company selling x x units is given by the quadratic function: P(x)=1200x2+30x P(x) = -\frac{1}{200}x^{2} + 30x Which of the following equivalent expressions displays the break-even point as a constant or coefficient? Choose 11 answer: (A)1200((x3,000)29,000,000) (A) -\frac{1}{200}((x-3,000)^{2}-9,000,000) (B)12.00(x3,000)2+45,000 (B) -\frac{1}{2.00}(x-3,000)^{2}+45,000 1313 of 1313 Skip Check ENG US (j)) 202420240-0

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Q. Khan Academy Donate ^{(33)} embongw s blazing! 22 week streak Level 1515 111111//111111 skills Production is profitable only when revenue is greater than cost. The monthly profit of a company selling x x units is given by the quadratic function: P(x)=1200x2+30x P(x) = -\frac{1}{200}x^{2} + 30x Which of the following equivalent expressions displays the break-even point as a constant or coefficient? Choose 11 answer: (A)1200((x3,000)29,000,000) (A) -\frac{1}{200}((x-3,000)^{2}-9,000,000) (B)12.00(x3,000)2+45,000 (B) -\frac{1}{2.00}(x-3,000)^{2}+45,000 1313 of 1313 Skip Check ENG US (j)) 202420240-0
  1. Rewrite function in vertex form: Step 11: Given function: P(x)=1200x2+30x P(x) = -\frac{1}{200}x^2 + 30x Rewrite the function in vertex form.
  2. Complete the square: Step 22: Complete the square: P(x) = -\left(\frac{11}{200200}\right)(x^22 - 60006000x)
  3. Add and subtract values: Step 33: Add and subtract (60002)2(\frac{6000}{2})^2 inside the parentheses: P(x)=(1200)(x26000x+90000009000000)P(x) = -\left(\frac{1}{200}\right)(x^2 - 6000x + 9000000 - 9000000)
  4. Factor and simplify: Step 44: Factor the perfect square trinomial and simplify: P(x)=(1200)((x3000)29000000)P(x) = -\left(\frac{1}{200}\right)\left((x - 3000)^2 - 9000000\right)
  5. Distribute 1200-\frac{1}{200}: Step 55: Distribute the 1200-\frac{1}{200}: P(x)=(1200)(x3000)2+45,000P(x) = -\left(\frac{1}{200}\right)(x - 3000)^2 + 45,000
  6. Compare with choices: Step 66: Compare with given choices: (A) 1200((x3,000)29,000,000)-\frac{1}{200}((x-3,000)^2 - 9,000,000) (B) 1200(x3,000)2+45,000-\frac{1}{200}(x-3,000)^2 + 45,000
  7. Identify break-even point: Step 77: Identify the expression with the break-even point as a constant or coefficient: Answer is (B) 1200(x3,000)2+45,000-\frac{1}{200}(x-3,000)^2 + 45,000

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