Answer:
[tex]y = - 3.0625[/tex]
Step-by-step explanation:
The given parabola has equation:
[tex] \frac{1}{4} (y + 3) = {(x - 2)}^{2} [/tex]
Or
[tex]{(x - 2)}^{2} = \frac{1}{4} (y + 3)[/tex]
We compare this to
[tex] {(x - h)}^{2} = 4p(y - k)[/tex]
[tex] \implies \: 4p = \frac{1}{4} [/tex]
[tex]p = \frac{1}{4} \div 4[/tex]
[tex]p = \frac{1}{4} \times \frac{1}{4} [/tex]
[tex]p = \frac{1}{16} [/tex]
The vertex of this parabola is (2,-3)
The directrix is p units below the y-value of the vertex
[tex]y = - 3 - \frac{1}{16} = - 3.0625[/tex]
