9. What are the zeros of the quadratic function shown below? \[ y=(x-m)(x+n) \] a. \( m \) and \( n \) b. \( -m \) and \( n \) c. \( m \) and \( -n \) d. The zeros cannot be determined for the function.
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The zeros of the quadratic function \( y = (x - m)(x + n) \) can be found by setting the function equal to zero. This leads to the equation \( (x - m)(x + n) = 0 \). Solving this gives us the zeros \( x = m \) and \( x = -n \). So, the right answer is not directly listed. However, recognizing the structure of the equation helps us derive them easily! Understanding how to find zeros can be particularly useful in various real-world applications, such as physics for determining points of equilibrium or in finance for calculating break-even points in business. Exploring quadratic functions can really lend itself to practical situations where identifying those crucial 'zero' points becomes necessary for decision-making and strategy!
