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.

To find the zeros of the quadratic function \( y=(x-m)(x+n) \), we set \( y=0 \). This gives us the equation \( (x-m)(x+n) = 0 \). Hence, the zeros occur when either \( x-m=0 \) or \( x+n=0 \), leading to the solutions \( x=m \) and \( x=-n \). So, the correct answer involves the values \( m \) and \( -n \). Exploring further, the zeros of a quadratic function are the x-values where the graph intersects the x-axis. This means they play a crucial role in understanding the behavior of the function. If you graph \( y=(x-m)(x+n) \), the points at which the parabola touches or crosses the x-axis correspond directly to these zeros, giving insight into how the quadratic unfolds. As a handy tip in identifying the zeros, remember that if you have a factored form like this function, the zeros are simply the values of \( x \) that make each factor equal to zero. Just be cautious—it's common to confuse signs or mix up the variables when substituting! Always double-check your work to avoid those little slip-ups.