document.write( "Question 544669: I need help with this problem. It states that given that a parabola has a directrix of y= -3.25 and focus (0,-2.75), find the vertex. Then it wants me to write the equation of the parabola then graph the parabola. \n" ); document.write( "
Algebra.Com's Answer #355202 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Given that a parabola has a directrix of y= -3.25 and focus (0,-2.75), find the vertex.
\n" ); document.write( "Write the equation of the parabola then graph the parabola.
\n" ); document.write( "**
\n" ); document.write( "Standard form of equation of given parabola: (x-h)^2=4p(y-k), (h,k)=(x,y) coordinates of vertex.
\n" ); document.write( "..
\n" ); document.write( "Since the given x-coordinate of the focus=0, the axis of symmetry is x=0.
\n" ); document.write( "And since the focus is above the directrix, the parabola opens upwards.
\n" ); document.write( "x-coordinate of vertex=x-coordinate of the focus=0
\n" ); document.write( "y-coordinate of vertex is midway between focus and directrix on the axis of symmetry:
\n" ); document.write( "(-3.25-2.75)/2=-6/2=-3
\n" ); document.write( "vertex:(0,3)
\n" ); document.write( "p=distance from vertex to focus or to directrix on the axis of symmetry=-3 to-2.75=.25
\n" ); document.write( "4p=.25=1/4
\n" ); document.write( "p=1/16
\n" ); document.write( "Equation of given parabola:
\n" ); document.write( "(x-0)^2=(1/16)(y+3)
\n" ); document.write( "x^2=(y+3)/16
\n" ); document.write( "..
\n" ); document.write( "see graph below as a visual check on answers above:
\n" ); document.write( "y=16x^2-3
\n" ); document.write( "\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C16x%5E2-3%29+\" \n" ); document.write( "
\n" );