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what is the focus the parabola?
with a vertex at (-2,14), containing points (-3,12) and (-1,12)?
1 Answer
- DWReadLv 71 decade agoFavorite Answer
(-3, 12) and (-1, 12) have the same y-coordinate, indicating a vertical parabola with axis of symmetry x = -2
These points lie below the vertex (-2, 14), so the parabola opens downwards.
General equation for a down-opening parabola:
y = -a(x-h)² + k, with vertex (h, k)
In your equation, (h, k) = (-2, 14). The equation becomes
y = -a(x+2)² + 14
Use one of the points to solve for a.
12 = -a(-3+2)²+13
12 = -a + 13
a = 1
The equation becomes
y = (x+2)²+14
p = 1/(4a) = ¼
focus (-2, 14-p) = (-2, 13¾)
