document.write( "Question 1106239: What is the equation in standard form of a parabola whose vertex is (3,-1) and whose directrix is x=-2 ?
\n" ); document.write( "1.(y+1)^2=20(x-3)
\n" ); document.write( "2.(x+3)^2=20(y+1)
\n" ); document.write( "3.(x-3)^2=20(y+1)
\n" ); document.write( "4.(y-1)^2=20(x+3) \n" ); document.write( "
Algebra.Com's Answer #721236 by greenestamps(13203)\"\" \"About 
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\n" ); document.write( "The directrix is a vertical line, and it is to the left of the vertex, so the parabola opens to the right. That means the y variable is squared and the x variable is not. Since the question as you show it is multiple choice, that eliminates answer choices 2 and 3.

\n" ); document.write( "Note that NONE of the answer choices are in standard form. Standard form for a parabola opening right or left would be \"x+=+ay%5E2%2Bby%2Bc\". The answer choices are all in VERTEX form.

\n" ); document.write( "For a parabola that opens right or left, the vertex form of the equation contains (y-k)^2 and (x-h), where (h,k) is the vertex. Since the vertex is given to be (3,-1), the equation must contain \"(y+1)^2\" and \"(x-3)\". Again since the problem is multiple choice, there is only one answer choice which could possibly be the right equation -- answer choice 1.

\n" ); document.write( "To see that answer choice 1 is in fact the right equation, you need to look at the vertex form more closely. For a parabola opening to the right, the vertex form of the equation is

\n" ); document.write( "\"%28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2\"

\n" ); document.write( "In this form, the vertex is (h,k), and p is the distance from the vertex to the directrix and from the vertex to the focus.

\n" ); document.write( "Answer choice 1 in vertex form is

\n" ); document.write( "\"%28x-3%29+=+%281%2F20%29%28y%2B1%29%5E2\"

\n" ); document.write( "So 4p=20, which means p is 5. And the directrix x=-2 is indeed 5 units to the left of the vertex; so answer choice 1 is the correct equation for the parabola. \n" ); document.write( "
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