Khan Academy Donate ^{(3)} embongw s blazing! 2 week streak Level 15111//111 skills 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)=−2001x2+30x Which of the following equivalent expressions displays the break-even point as a constant or coefficient? Choose 1 answer: (A)−2001((x−3,000)2−9,000,000)(B)−2.001(x−3,000)2+45,00013 of 13 Skip Check ENG US (j)) 2024−0
Q. Khan Academy Donate ^{(3)} embongw s blazing! 2 week streak Level 15111//111 skills 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)=−2001x2+30x Which of the following equivalent expressions displays the break-even point as a constant or coefficient? Choose 1 answer: (A)−2001((x−3,000)2−9,000,000)(B)−2.001(x−3,000)2+45,00013 of 13 Skip Check ENG US (j)) 2024−0
Rewrite function in vertex form: Step 1: Given function: P(x)=−2001x2+30x Rewrite the function in vertex form.
Complete the square: Step 2: Complete the square: P(x) = -\left(\frac{1}{200}\right)(x^2 - 6000x)
Add and subtract values: Step 3: Add and subtract (26000)2 inside the parentheses: P(x)=−(2001)(x2−6000x+9000000−9000000)
Factor and simplify: Step 4: Factor the perfect square trinomial and simplify: P(x)=−(2001)((x−3000)2−9000000)
Distribute −2001: Step 5: Distribute the −2001: P(x)=−(2001)(x−3000)2+45,000
Compare with choices: Step 6: Compare with given choices: (A) −2001((x−3,000)2−9,000,000) (B) −2001(x−3,000)2+45,000
Identify break-even point: Step 7: Identify the expression with the break-even point as a constant or coefficient: Answer is (B) −2001(x−3,000)2+45,000
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