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Question 757090: A parabola has vertex (2,4) and directrix at y=8. Find the x-intercepts of the parabola.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A parabola has vertex (2,4) and directrix at y=8. Find the x-intercepts of the parabola.
Given parabola opens downward.(directrix is above vertex on the axis of symmetry)
Its basic equation: (x-h)^2=-4p(y-k)
Given vertex: (2,4)
axis of symmetry: x=2
p=4 (distance from vertex to directrix on the axis of symmetry)
4p=16
Equation of given parabola:
(x-2)^2=-16(y-4)
To find x-intercepts, set y=0
(x-2)^2=-16(-4)=64
x-2=±√64=±8
x=2±8
x=-6, 10
x-intercepts are:-6 and 10
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