Solving Quadratic Inequalities

Nathan is a product manager for a home security company. Through testing and focus groups, he has modeled the equation P = -(x - 32)2 + 1000 to represent the profit (in thousands) of the price x for a new home security camera. Find the prices in dollars at which Nathan can make a profit of at least $471, 000. Show your work as it is done in the lesson content and include units of measurement.. HINT: Use 471 as part of the inequality you set up, not 471,000.

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raphealnwobi raphealnwobi · Answer 1 · 2022-07-11T18:31:47+02:00

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:

-(x - 32)² + 1000 ≥ 471

-(x² - 64x + 1024) + 1000 ≥ 471

-x² + 64x - 1024 + 1000 - 471 ≥ 0

-x² + 64x - 495 ≥ 0

x = 55 or x = 9

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

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