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Question 833799: suppose a parabola has an axis of symmetry at x=1, a maximum height of 6 and also through the point (2,4). write the equation of the parabola in vertex form
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! suppose a parabola has an axis of symmetry at x=1, a maximum height of 6 and also through the point (2,4). write the equation of the parabola in vertex form
.
Vertex form of a parabola is:
y = a(x-h)^2 + k
where
(h,k) is the vertex
.
Since the "axis of symmetry is at x=1"
the 'h' value must be 1
since the max height is at 6
the 'k' value must be 6
so, now we have
y = a(x-1)^2 + 6
.
to find 'a', plug in (2,4) and solve for 'a':
y = a(x-1)^2 + 6
4 = a(2-1)^2 + 6
4 = a(1)^2 + 6
-2 = a(1)
-2 = a
.
answer:
y = -2(x-1)^2 + 6
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