document.write( "Question 533794: find the vertex, focus, and directrix of the following parabola. then draw the grapg. (x-3)^2=-5(y+1) \n" ); document.write( "

Algebra.Com's Answer #351212 by lwsshak3(11628) $\"\"$ $\"About$

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find the vertex, focus, and directrix of the following parabola. then draw the grapg. (x-3)^2=-5(y+1)
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\n" ); document.write( "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.
\n" ); document.write( "For given equation: (x-3)^2=-5(y+1)
\n" ); document.write( "vertex: (3,-1)
\n" ); document.write( "4p=5
\n" ); document.write( "p=5/4 (distance down from vertex to focus on axis of symmetry, x=3
\n" ); document.write( "focus:(3,(-1-p))=(3,(-1-(5/4))=(3,-9/4)
\n" ); document.write( "directrix: y=-1+(5/4)=1/4 (a horizontal line p units up from the vertex on the axis of symmetry
\n" ); document.write( "y-intercept:
\n" ); document.write( "set x=0
\n" ); document.write( "3^2=-5y-5
\n" ); document.write( "9+5=-5y
\n" ); document.write( "y=-14/5=2.8
\n" ); document.write( "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 \n" ); document.write( "

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