Answer:
[tex]y = - {(x - 4)}^{2} - 2[/tex]
[tex]y = - {(x + 4)}^{2} - 2[/tex]
[tex]y = - {x}^{2} - 2[/tex]
Step-by-step explanation:
A vertex form equation of a parabola is of the form
[tex]y = a(x - h)^{2} + k[/tex]
with vertex at (h,k).
If a parabola opens downwards, then a<0.
If the vertex of such parabola is below the x-axis, then it has no real solution, because it will not intersect the x-axis.
[tex]y = - {(x + 4)}^{2} - 2[/tex]
has vertex at (-4,-2), which is below x-axis.
[tex]y = - {(x - 4)}^{2} + 2[/tex]
has vertex at (-4,2)--->above x-axis
[tex]y = - {(x - 4)}^{2} - 2[/tex]
vertex at (4,-2) ---> below x-axis
[tex]y = - {x }^{2} - 2[/tex]
(0,-2)----> below x-axis
