document.write( "Question 993650: Please help me with this problem also:
\n" ); document.write( "Find the coordinates of the focus and the equation of the directrix of the parabola which crosses the x axis at x = -1 and x = 3 and which crosses the y axis at y = -12.[ Hint: first find the equation of the parabola and then write it in the form $\"%28x+-+h%29%5E2\"$ = 4p(y - k).] \r
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Algebra.Com's Answer #612916 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
You can adjust the form after you find the equation using your given data.\r
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\n" ); document.write( "\n" ); document.write( "You have an unknown factor, \"a\" which fits $\"y=a%28x-%28-1%29%29%28x-3%29\"$
\n" ); document.write( " $\"y=a%28x%2B1%29%28x-3%29\"$
\n" ); document.write( "and then
\n" ); document.write( " $\"a%28x%2B1%29%28x-3%29=y\"$
\n" ); document.write( " $\"a%280%2B1%29%280-3%29=-12\"$
\n" ); document.write( " $\"a%2A1%2A%28-3%29=-12\"$
\n" ); document.write( " $\"a=-12%2F%28-3%29\"$
\n" ); document.write( " $\"a=4\"$
\n" ); document.write( "For the equation $\"highlight_green%28y=4%28x%2B1%29%28x-3%29%29\"$ . This is in FACTORED form, but you next want to adjust into Standard Form, using simplification and then Completing The Square.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%28x%5E2-2x-3%29\"$
\n" ); document.write( "and the term to add and subtract inside the parentheses will be 1.
\n" ); document.write( "Why, see this Lesson includes how to complete the square to put into standard form.
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\n" ); document.write( " $\"y=4%28x%5E2-2x%2B1-1-3%29\"$
\n" ); document.write( " $\"y=4%28%28x-1%29%5E2-4%29\"$
\n" ); document.write( " $\"y=4%28x-1%29%5E2-16\"$ -----Standard Form
\n" ); document.write( "and then
\n" ); document.write( " $\"highlight%28y%2B16=4%28x-1%29%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now you want to determine the focus and directrix. I suggest you check these two video presentations which explain this more:
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\n" ); document.write( "parabola, directrix and focus, with the vertex at origin
\n" ); document.write( "-
\n" ); document.write( "parabola equation using focus and directrix but now vertex not at origin\r
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\n" ); document.write( "\n" ); document.write( "Understand that your equation put into the appropriate form will be $\"highlight%28%28x-1%29%5E2=%281%2F4%29%28y%2B16%29%29\"$ and in this way, your $\"4p\"$ will be equal to $\"1%2F4\"$ , and you can find the value and meaning for p. \n" ); document.write( "

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