1. **State the problem:** We need to find which quadratic function has solutions $x=8$ and $x=-5$. 2. **Recall the factored form of a quadratic:** If the roots are $r_1$ and $r_2$, the quadratic can be written as $$y = (x - r_1)(x - r_2) = 0.$$ For roots $8$ and $-5$, this becomes $$y = (x - 8)(x + 5).$$ 3. **Expand the factored form:** $$y = x^2 + 5x - 8x - 40 = x^2 - 3x - 40.$$ 4. **Compare with given options:** - Option a: $y = x^2 + 3x - 40$ - Option b: $y = x^2 - 3x - 40$ The expanded form matches option b. **Final answer:** The quadratic function with solutions $x=8$ and $x=-5$ is $$y = x^2 - 3x - 40.$$