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Answer:
focus : (3,-1.5)
directrix : x = 1
Step-by-step explanation:
The focus is located p units horizontally from the vertex. If the parabola opens to the right, the focus is at (h + p , k ) . If it opens to the left, the focus is at ( h − p , k ) .
The directrix is a vertical line located p units horizontally from the vertex. If the parabola opens to the right, the directrix is the line x = h − p. If it opens to the left, the directrix is the line x = h + p.
Solving:
[tex]\[(y + 1.5)^2 = 4(x - 2)\][/tex]
[tex]\[h = 2, \quad k = -1.5, \quad 4p = 4 \implies\boxed{ p = 1}\][/tex]
[tex]\[\text{Vertex} = (2, -1.5)\][/tex]
[tex]\(p = 1\) \text{and the parabola expands to the right the focus is: } \\\\\((2 + 1, -1.5) =\boxed{ (3, -1.5)}[/tex]
[tex]\text{The directrix is the vertical line}~ \(x = 2 - 1 = 1\).\\\\\boxed{x = 1}[/tex]