Find 2 numbers with minimum product

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Taught by YourMathGal
  • Currently 4.0/5 Stars.
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Lesson Summary:

In this lesson, we learn how to find two numbers whose difference is 6 and whose product is as small as possible. We explore different possibilities and then solve the problem algebraically by using a quadratic equation and the vertex point. The smallest product is found to be -9, which corresponds to the numbers 3 and -3, whose difference is indeed 6. This lesson provides a great way to practice problem-solving skills and algebraic techniques in a fun and engaging way.

Lesson Description:

We do this problem: Find 2 numbers whose difference is 6 and whose product is as small as possible. This is done using a quadratic equation and the vertex point.

More free YouTube videos by Julie Harland are organized at http://yourmathgal.com

Questions answered by this video:
  • How do you find 2 numbers whose difference is 6 and whose product is as small as possible?
  • How do you find the 2 numbers that minimize their product and have a given sum or difference?
  • How do you find the vertex of y = x(x + 6)?
  • What is the vertex of y = x^2 + 6x?
  • Staff Review

    • Currently 4.0/5 Stars.
    This lesson is another example of using a parabola to find a minimum or maximum in a word problem. In this case, the goal is to minimize the product of two numbers when their difference is 6. An equation is set up and the vertex is found in order to solve this problem. All steps involved are explained.