1. The problem asks to find the number of x-intercepts of the graph of the function $y = x^2 + 5x - 1$. 2. To find x-intercepts, we set $y=0$ and solve the quadratic equation: $$x^2 + 5x - 1 = 0$$ 3. We use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=5$, and $c=-1$. 4. Calculate the discriminant: $$\Delta = b^2 - 4ac = 5^2 - 4 \times 1 \times (-1) = 25 + 4 = 29$$ 5. Since $\Delta > 0$, there are two distinct real roots, meaning two x-intercepts. 6. Find the roots: $$x = \frac{-5 \pm \sqrt{29}}{2}$$ 7. Therefore, the graph of $y = x^2 + 5x - 1$ has 2 x-intercepts.