document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208475>Question 208475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help.I posted these about 3 days ago,but  haven't got a response.Can someone please help.thanks\r<BR>\n" );
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document.write( "a parabola that opens to the right is a ? a. radicand b. function c.linear equation d. relation\r<BR>\n" );
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document.write( "sketch the graphs using the roots to find the function and the turning point<BR>\n" );
document.write( "(1).x= -8, x=4<BR>\n" );
document.write( "(2)x= -3,x=3\r<BR>\n" );
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document.write( "use algebra to show that there are no common solutions.<BR>\n" );
document.write( "(1)y = f(x)= x^2 + 4<BR>\n" );
document.write( "   y = x - 5\r<BR>\n" );
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document.write( "(2) y = f(x) = -2x^2<BR>\n" );
document.write( "    y = 4\r<BR>\n" );
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document.write( "find the common solution for each pair of linear equations\r<BR>\n" );
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document.write( "(1) 4y + 3x = 12<BR>\n" );
document.write( "    2x + 3y = 1\r<BR>\n" );
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document.write( "thank you for your time and help.I really appreciate it.<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 #157699 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=157699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a parabola that opens to the right is a ? <BR>\n" );
document.write( "a. radicand <BR>\n" );
document.write( "b. function <BR>\n" );
document.write( "c.linear equation <BR>\n" );
document.write( "d. relation<BR>\n" );
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document.write( "Ans: It is a relation because there are two y values for each x-value<BR>\n" );
document.write( "in the domain.<BR>\n" );
document.write( "----------------------------------------------- <BR>\n" );
document.write( "sketch the graphs using the roots to find the function and the turning point<BR>\n" );
document.write( "(1).x= -8, x=4<BR>\n" );
document.write( "Ans: f(x) = (x+8)(x-4) = x^2 +4x -32<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B8%29%28x-4%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B8%29%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Roots are x = -8 and 4<BR>\n" );
document.write( "Turning point occurs at x = -b/2a = -4/2 = -2<BR>\n" );
document.write( "Turning point y-value is f(-2) = (6)*(-6) = -36<BR>\n" );
document.write( "Turning point is (-2,-36)<BR>\n" );
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document.write( "(2)x= -3,x=3 <BR>\n" );
document.write( "Ans: y = (x+3)(x-3) = x^2 -9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-9%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Roots are x = -3 and 3<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Turning point occurs at x = -b/2a = -0/2 = 0<BR>\n" );
document.write( "f(0) = -9<BR>\n" );
document.write( "Turning point is (0,-9)<BR>\n" );
document.write( "--------------------------------------------------------------<BR>\n" );
document.write( "use algebra to show that there are no common solutions.<BR>\n" );
document.write( "(1)y = x^2 + 4<BR>\n" );
document.write( "y = x - 5 <BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute for \"y\" to get:<BR>\n" );
document.write( "x^2+4 = x-5<BR>\n" );
document.write( "x^2 - x + 9 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The determinant is b^2-4ac = 1-4*9 = -35<BR>\n" );
document.write( "Since the determinant is negative there are no Real Number solutions.<BR>\n" );
document.write( "Therefore there are no points of intersection.<BR>\n" );
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document.write( "(2) y = -2x^2<BR>\n" );
document.write( "y = 4<BR>\n" );
document.write( "Substitute to get -2x2 = 4<BR>\n" );
document.write( "2x^2+4 = 0<BR>\n" );
document.write( "x^2 + 2 = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "b^2 - 4ac = 0-4*2*1 is negative<BR>\n" );
document.write( "No solutions and no points of intersection.<BR>\n" );
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document.write( "find the common solution for each pair of linear equations <BR>\n" );
document.write( "(1) 4y + 3x = 12<BR>\n" );
document.write( "....2x + 3y = 1<BR>\n" );
document.write( "Ans:<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "3x + 4y = 12<BR>\n" );
document.write( "2x + 3y = 1<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Multiply thru the 1st Eq. by 2 and the 3nd equation by 3 to get:<BR>\n" );
document.write( "6x + 8t = 24<BR>\n" );
document.write( "6x + 9y = 3<BR>\n" );
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document.write( "Subtract 1st from 2nd to get:<BR>\n" );
document.write( "y = -21<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Substitute into 2x + 3y = 1 to solve for \"x\":<BR>\n" );
document.write( "2x + 3*-21 = 1<BR>\n" );
document.write( "2x -63 = 1<BR>\n" );
document.write( "2x = 64<BR>\n" );
document.write( "x = 32<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solution: (32,-21)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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