\#8 \( \begin{array}{c}f(x)=x^{2}-8 x+15 \\ x^{2}-8 x+15=0\end{array} \)

To solve the equation \( x^2 - 8x + 15 = 0 \), we can factor it. The equation factors into \( (x-3)(x-5) = 0 \). Therefore, the solutions are \( x = 3 \) and \( x = 5 \). This means the parabola represented by the function f(x) crosses the x-axis at these points. Now let's quickly discuss the vertex of the parabola given by \( f(x) \). The vertex form can be derived by completing the square, yielding the vertex at \( (4, -1) \). This point represents the minimum value of the function, as the parabola opens upwards. Keep it in mind for graphing or interpreting the function's behavior!