The x-intercepts are when y=0, so:
[tex]x^2 + 4x-6=0\\\\x=\frac{-4 \pm \sqrt{4^{2}-4(1)(-6)}}{2}\\\\x=\frac{-4 \pm \sqrt{40}}{2}\\\\x=-2 \pm \sqrt{10}[/tex]
So, the x-intercepts are at [tex]\boxed{(-2 \pm \sqrt{10}, 0)}[/tex]
The y-intercept is when x=0, so [tex]y=0^{2}+4(0)-6[/tex], and thus the y-intercept is at (0, -6).
