Factor. \[ y^{2}-8 y+15 \] \( \square \)

To factor the quadratic expression \( y^{2} - 8y + 15 \), we look for two numbers that multiply to 15 (the constant term) and add up to -8 (the coefficient of the linear term). Those two numbers are -3 and -5. Therefore, we can rewrite the expression as \( (y - 3)(y - 5) \). Thus, the factored form is: \[ (y - 3)(y - 5) \] Now, let’s find the roots of this equation, which are simply the values of \( y \) that make either factor equal to zero. By setting each factor to zero, we find \( y = 3 \) and \( y = 5 \). This tells us that the parabola defined by the quadratic equation touches the x-axis at these points, providing insight into its graph!