document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=623928>Question 623928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need someone help i am stuck doing this last part of my homework. can someone explain it to me \r<BR>\n" );
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document.write( "Match each equation for a parabola with the direction that the parabola opens.\r<BR>\n" );
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document.write( "1. y=-3(x+1)^2-8                <BR>\n" );
document.write( "2. x=-3(y+1)^2-8<BR>\n" );
document.write( "3. y=3(x+1)^2-8<BR>\n" );
document.write( "4. x=3(y+1)^2-8\r<BR>\n" );
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document.write( "A. up<BR>\n" );
document.write( "B. right<BR>\n" );
document.write( "C. down<BR>\n" );
document.write( "D. left \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #392414 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=392414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if y = x^2, then the parabola will open up.<BR>\n" );
document.write( "if y = -x^2, then the parabole will open down.<BR>\n" );
document.write( "if x = y^2, then the parabola will open to the right.<BR>\n" );
document.write( "if x = -y^2, then the parabole will open to the left.<BR>\n" );
document.write( "what we are dealing with is the coefficient of the squared term.<BR>\n" );
document.write( "your equations are:<BR>\n" );
document.write( "1. y=-3(x+1)^2-8<BR>\n" );
document.write( "2. x=-3(y+1)^2-8<BR>\n" );
document.write( "3. y=3(x+1)^2-8<BR>\n" );
document.write( "4. x=3(y+1)^2-8 <BR>\n" );
document.write( "(x+1)^2 will be equal to x^2 + 2x + 1<BR>\n" );
document.write( "(y+1)^2 will be equal to y^2 + 2y + 1<BR>\n" );
document.write( "your equations therefore become:<BR>\n" );
document.write( "1. y = -3(x^2 + 2x + 1) - 8<BR>\n" );
document.write( "2. x = -3(y^2 + 2y + 1) - 8<BR>\n" );
document.write( "3. y = 3(x^2 + 2x + 1) - 8<BR>\n" );
document.write( "4. x = 3(y^2 + 2y + 1) - 8<BR>\n" );
document.write( "remove parentheses and simplify to get:<BR>\n" );
document.write( "1. y = -3x^2 - 6x - 11<BR>\n" );
document.write( "2. x = -3y^2 - 6y - 11<BR>\n" );
document.write( "3. y = 3x^2 + 6x - 5 <BR>\n" );
document.write( "4. x = 3y^2 + 3y - 5<BR>\n" );
document.write( "when determining whether the parabole will open up or down, the only meaningful consideration is the sign of the coefficient of the squared term.<BR>\n" );
document.write( "based on this, you should get the following answers.<BR>\n" );
document.write( "1. will open down<BR>\n" );
document.write( "2. will open to the left.<BR>\n" );
document.write( "3. will open up.<BR>\n" );
document.write( "4. will open to the right.<BR>\n" );
document.write( "we can graph these equations and see how we did.<BR>\n" );
document.write( "to graph these equations, you have to solve for y in all equations.<BR>\n" );
document.write( "the original equations are:<BR>\n" );
document.write( "1. y=-3(x+1)^2-8<BR>\n" );
document.write( "2. x=-3(y+1)^2-8<BR>\n" );
document.write( "3. y=3(x+1)^2-8<BR>\n" );
document.write( "4. x=3(y+1)^2-8 <BR>\n" );
document.write( "equations 1 and 3 can be graphed as is.<BR>\n" );
document.write( "you need to solve for y in equations 2 and 4.<BR>\n" );
document.write( "equation 2 is:<BR>\n" );
document.write( "x = -3(y+1)^2 - 8<BR>\n" );
document.write( "add 3(y+1)^2 to both sides of this equation and subtract x from both sides of this equation to get:<BR>\n" );
document.write( "3(y+1)^2 = -x - 8<BR>\n" );
document.write( "divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "(y+1)^2 = (-x-8)/3 which is the same as:<BR>\n" );
document.write( "(y+1)^2 = -(x+8)/3<BR>\n" );
document.write( "take the square root of both sides of this equation to get:<BR>\n" );
document.write( "y+1 = +/- ( -(x+8)/3 )<BR>\n" );
document.write( "subtract 1 from both sides of this equation to get:<BR>\n" );
document.write( "y = -1 +/- sqrt( -(x+8)/3 )<BR>\n" );
document.write( "equations to graph for equation 2 are:<BR>\n" );
document.write( "y = -1 + sqrt( -(x+8)/3 )<BR>\n" );
document.write( "y = -1 - sqrt( -(x+8)/3 )<BR>\n" );
document.write( "equation 4 is:<BR>\n" );
document.write( "x = 3(y+1)^2 - 8<BR>\n" );
document.write( "add 8 to both sides of this equation to get:<BR>\n" );
document.write( "3(y+1)^2 = x + 8<BR>\n" );
document.write( "divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "(y+1)^2 = (x+8)/3<BR>\n" );
document.write( "take the square root of both sides of this equation to get:<BR>\n" );
document.write( "y+1 = +/- sqrt( (x+8)/3 )<BR>\n" );
document.write( "subtract 1 from both sides of this equation to get:<BR>\n" );
document.write( "y = -1 +/- sqrt( (x+8)/3 )<BR>\n" );
document.write( "equations to graph for equation 4 are:<BR>\n" );
document.write( "y = -1 + sqrt( (x+8)/3 )<BR>\n" );
document.write( "y = -1 - sqrt( (x+8)/3 )<BR>\n" );
document.write( "graph of equation 1 is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-30%2C30%2C-3%28x%2B1%29%5E2-8%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-30%2C30%2C-3%28x%2B1%29%5E2-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "graph of equation 2 is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-30%2C30%2C-5%2C5%2C-1+%2B+sqrt%28+-%28x%2B8%29%2F3+%29%2C-1+-+sqrt%28+-%28x%2B8%29%2F3+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "graph of equation 3 is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-30%2C30%2C3%28x%2B1%29%5E2-8%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-30%2C30%2C3%28x%2B1%29%5E2-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "graph of equation 4 is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-30%2C30%2C-5%2C5%2C-1+%2B+sqrt%28+%28x%2B8%29%2F3+%29%2C-1+-+sqrt%28+%28x%2B8%29%2F3+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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