1. The problem asks to find the discriminant of the quadratic equation selected in question #1, which is $y = x^2 - 13x + 40$. 2. The quadratic formula is $ax^2 + bx + c = 0$, and the discriminant $\Delta$ is given by: $$\Delta = b^2 - 4ac$$ 3. For the equation $x^2 - 13x + 40 = 0$, the coefficients are: - $a = 1$ - $b = -13$ - $c = 40$ 4. Calculate the discriminant: $$\Delta = (-13)^2 - 4 \times 1 \times 40 = 169 - 160 = 9$$ 5. The discriminant is 9, which is positive and a perfect square, indicating there are two distinct real solutions. 6. This matches the given solutions $x = 8$ and $x = -5$ because a positive discriminant means two real roots. Final answer: The discriminant is $9$, confirming two real solutions as given.