document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257102>Question 257102</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decide on ANY ONE quadratic function of your choice whose graph will be a parabola. 1. Will your team's parabola open upwards or downwards?Why? <BR>\n" );
document.write( "2. What’s the vertex of your team's parabola? \r<BR>\n" );
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document.write( "3. What’s the x-intercepts of your team's parabola? \r<BR>\n" );
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document.write( "4. Can you ever have parabolas that open to the left or which open to the right?Why?\r<BR>\n" );
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document.write( "Can someone please help me solvve this? I have submitted this question several times and no one has answered it. Thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189079 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I will give you an answer. Here is the question:<BR>\n" );
document.write( "1. Will your team's parabola open upwards or downwards? Why? <BR>\n" );
document.write( "ANSWER: First all parabolas have the general equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where (h,k) is the vertex.<BR>\n" );
document.write( "The open up / down part depends on the parabola you have chosen. If you choose a<0 it will open down. If you choose a > 0, it will open up. Why? with a > 0, you are generating positive numbers times squared numbers which are positive numbers. So they will increase as x increases. With a < 0, you are generating negative numbers times squared numbers which are positive numbers. So they will decrease as x increases.<BR>\n" );
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document.write( "2. What’s the vertex of your team's parabola? <BR>\n" );
document.write( "ANSWER: The vertex of any parabola in general is (h,k)<BR>\n" );
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document.write( "3. What’s the x-intercepts of your team's parabola? <BR>\n" );
document.write( "ANSWER: in order to find the x-intercepts, we need the general quadratic formula as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2+%2B+Bx+%2B+C+=+0 ALIGN=MIDDLE  ALT=\"Ax%5E2+%2B+Bx+%2B+C+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If we apply the quadratic formula, we get in general,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "4. Can you ever have parabolas that open to the left or which open to the right?Why? <BR>\n" );
document.write( "ANSWER: Yes, we can have these they are called sleeping parabolas. To get these, reverse the x and y variables as the following:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a%28y-k%29%5E2+%2B+h ALIGN=MIDDLE  ALT=\"x+=+a%28y-k%29%5E2+%2B+h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "EX: Y = -2(X - 4)^2 + 6<BR>\n" );
document.write( "This will open down since the front number is -.<BR>\n" );
document.write( "The vertex is (4,6)<BR>\n" );
document.write( "x-intercepts are: 4 +-sqrt(3)<BR>\n" );
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document.write( "Hope that answers your questions satisfactorily. </SPAN>\n" );
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