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

To find the x-intercept of the equation \( y = x^2 - 4x - 5 \), you set \( y \) equal to 0 and solve for \( x \). This gives you the equation \( 0 = x^2 - 4x - 5 \). Factoring the quadratic, you get \( (x - 5)(x + 1) = 0 \). Therefore, the x-intercepts are \( x = 5 \) and \( x = -1 \). You can also use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Substituting \( a = 1 \), \( b = -4 \), and \( c = -5 \) leads to the same solutions, proving that whether you factor or use the formula, you arrive at the same roots! How satisfying is that?