document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275837>Question 275837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)4x2 + 4x - 3<BR>\n" );
document.write( "I need help to find the intercepts, the vertex and the maximun or minimun.<BR>\n" );
document.write( "I know I need to use the quadratic formula, but I don't know how to apply it to find these three points.<BR>\n" );
document.write( "Thank you for your help.<BR>\n" );
document.write( "Martha </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201253 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=201253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 4x2 + 4x - 3<BR>\n" );
document.write( "I need help to find the intercepts, the vertex and the maximum or minimum.<BR>\n" );
document.write( "y = 4x^2 + 4x - 3<BR>\n" );
document.write( "The y intercept occurs when x=0<BR>\n" );
document.write( "y = 4(0) + 4(0) - 3<BR>\n" );
document.write( "y = -3 is the y intercept<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can use the quadratic formula to find the x intercepts<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this equation a=4, b=4, c=-3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%284%5E2-4%2A4%2A-3+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%284%5E2-4%2A4%2A-3+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%2816-%28-48%29+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%2816-%28-48%29+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%2816%2B48%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%2816%2B48%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%2864+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%2864+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+8%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+8%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F8 ALIGN=MIDDLE  ALT=\"4%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = .5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+8%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+8%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12%2F8 ALIGN=MIDDLE  ALT=\"-12%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = -1.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The x intercepts: x=.5, x=-1.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the vertex,<BR>\n" );
document.write( "first find the axis of symmetry using the formula x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"%28-4%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = -.5 <BR>\n" );
document.write( "The vertex occurs at x=-.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute that in the original equation for find y<BR>\n" );
document.write( "y = 4(-.5^2) + 4(-.5) - 3<BR>\n" );
document.write( "y = 4(.25) -2 - 3<BR>\n" );
document.write( "y = +1 - 2 - 3<BR>\n" );
document.write( "y = -4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Vertex: x=-.5,y=-4; and it is a minimum<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Looks like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+4%2C+-6%2C+4%2C+4x%5E2%2B4x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+4%2C+-6%2C+4%2C+4x%5E2%2B4x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "The intercepts and vertex should be apparent when you see it on this graph </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );