Question 533794: find the vertex, focus, and directrix of the following parabola. then draw the grapg. (x-3)^2=-5(y+1)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the vertex, focus, and directrix of the following parabola. then draw the grapg. (x-3)^2=-5(y+1)
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Given equation is that of a parabola of standard form: (x-h)^2=4p(y-k), (h,k) being the (x,y) coordinates of the vertex and parabola opens downward.
For given equation: (x-3)^2=-5(y+1)
vertex: (3,-1)
4p=5
p=5/4 (distance down from vertex to focus on axis of symmetry, x=3
focus:(3,(-1-p))=(3,(-1-(5/4))=(3,-9/4)
directrix: y=-1+(5/4)=1/4 (a horizontal line p units up from the vertex on the axis of symmetry
y-intercept:
set x=0
3^2=-5y-5
9+5=-5y
y=-14/5=2.8
This gives you two points, (0,-2.8) and (6,-2.8), in addition to the coordinates of the vertex, with which you can graph given equation
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