Answer:
Step-by-step explanation:
This is a positive parabola so it opens upwards. The equation for the directrix of this parabola is y = k - p. k is the second number in the vertex of the parabola which is (0, 0), but we need to solve for p.
The form that the parabola is currently in is
[tex]y=a(x-h)^2+k[/tex] so that means that [tex]a=\frac{1}{8}[/tex]. We can use that to solve for p in the formula
[tex]p=\frac{1}{4a}[/tex] so
[tex]p=\frac{1}{4(\frac{1}{8}) }[/tex] which simplifies to
[tex]p=\frac{1}{\frac{1}{2} }[/tex] which gives us that
p = 2. Now to find the directrix:
y = k - p becomes
y = 0 - 2 so
y = -2, choice A.
