find the x -intercept: \( y=x^{2}-4 x-5 \)

To find the x-intercept of the equation \( y = x^{2} - 4x - 5 \), you need to set \( y \) to zero and solve for \( x \). This gives you the equation \( 0 = x^{2} - 4x - 5 \). Factoring this gives you \( (x - 5)(x + 1) = 0 \). Therefore, the x-intercepts are \( x = 5 \) and \( x = -1 \). Did you know that the x-intercept represents the points where the graph of a function crosses the x-axis? For polynomial equations like this one, these points can indicate key changes in the direction of the parabola. In practical terms, if you're doing any graphical analysis or data interpretation, knowing the x-intercepts can help you determine the behavior of functions in various domains. For instance, this knowledge is critical in fields such as physics or economics when analyzing trajectories or profit-loss models!