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Answer:
y = -1/4x^2 -3/2x +3/4
Step-by-step explanation:
You know that vertex form is ...
y = (1/(4p))(x -h)^2 +k
for a focus-vertex distance of p and a vertex of (h, k).
Here, the focus-vertex distance is 2-3 = -1 (difference of y-coordinates), and the vertex is (h, k) = (-3, 3). This means the vertex form equation is ...
y = -1/4(x +3)^2 +3
Expanding the square gives ...
y = -1/4(x^2 +6x +9) +3
y = -1/4x^2 -3/2x +3/4
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<em>Additional comment</em>
The square of a binomial is ...
(x +a)^2 = x^2 +2ax +a^2
