Answer:
y = 1/8x² +5/4x +57/8
Explanation:
You want the standard form of the equation for the parabola with focus (-5, 6) and directrix y = 2.
Vertex
The vertex is halfway between the focus with coordinate y=6 and the directrix with equation y=2. Its y-coordinate will be (6+2)/2 = 4. It is 2 units below the focus, so p=2. The x-coordinate of the vertex is the same as that of the focus, so the vertex is (-5, 4).
Equation
The vertex form equation for the parabola is ...
y = 1/(4p)(x -h)² +k . . . . . . . vertex at (h, k)
y = 1/8(x +5)² +4 . . . . . . standard form in UK
Expanding this equation, we get ...
y = 1/8x² +5/4x +57/8 . . . . . . standard form in US
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Additional comment
The "standard form" of the equation for a parabola varies by location.
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