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Question 815611: Write the vertex form of the equation with the vertex at the origin, and the focus at (0,-1)
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! the vertex form of quadratic:
y = a(x − h)^2 + k
where (h,k) is the vertex, and is given as (0,0)
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vertex:
(vx, vy) given as (0,0)
vx = -b/2a = 0 therefore b = 0
vy = -D/4a = 0 therefore D = 0
NOTE: the formulas for vx and vy are well known and therefore given
D is the discriminant of the quadratic
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focus:
(fx, fy) given as (0,-1)
fx = -b/2a = 0 therefore b = 0
fy = (1 - D)/4a
NOTE: the formulas for fx and fy are well known and therefore given
D is the discriminant of the quadratic, but from the vertex work above, D = 0, so:
fy = 1/4a = -1
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therefore:
a = (-1/4)
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the vertex form of quadratic, again:
y = a(x − h)^2 + k
where (h,k) is the vertex, and is given as (0,0)
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Answer:
y = (-1/4)x^2
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