document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131679>Question 1131679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) Write the quadratic function rule that has a vertex at (-2,5) and is stretched by a factor of 2 and reflected across the x axis.\r<BR>\n" );
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document.write( "2) The vertex of a quadratic function is (1,-50). F(5) = -18. Find the function rule, find the roots, and find the y intercept.\r<BR>\n" );
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document.write( "3) The roots of a quadratic function are -3 and 7. The quadratic coefficient is -1/5. write the rule in factored form and find the maximum of the function </SPAN>\n" );
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document.write( "1) vertex at (-2,5); stretched by a factor of 2 and reflected across the x axis<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x%2B2%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"y+=+a%28x%2B2%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "with the stretch by a factor of 2 and a reflection across the x-axis, the coefficient a is -2.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2%28x%2B2%29%5E2%2B5 ALIGN=MIDDLE  ALT=\"y+=+-2%28x%2B2%29%5E2%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "2) vertex (1,-50); f(5) = -18<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-1%29%5E2-50 ALIGN=MIDDLE  ALT=\"y+=+a%28x-1%29%5E2-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "find the value of the coefficient a using the (x,y) coordinates of the given point, (5,-18).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18+=+a%285-1%29%5E2-50 ALIGN=MIDDLE  ALT=\"-18+=+a%285-1%29%5E2-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18+=+16a-50 ALIGN=MIDDLE  ALT=\"-18+=+16a-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32+=+16a ALIGN=MIDDLE  ALT=\"32+=+16a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2 ALIGN=MIDDLE  ALT=\"a+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%28x-1%29%5E2-50 ALIGN=MIDDLE  ALT=\"y+=+2%28x-1%29%5E2-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "roots: set y = 0 and solve.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2%28x-1%29%5E2-50 ALIGN=MIDDLE  ALT=\"0+=+2%28x-1%29%5E2-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-1%29%5E2+=+50 ALIGN=MIDDLE  ALT=\"2%28x-1%29%5E2+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=+5 ALIGN=MIDDLE  ALT=\"x-1+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=+-5 ALIGN=MIDDLE  ALT=\"x-1+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4 ALIGN=MIDDLE  ALT=\"x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The roots are 6 and -4.<br><BR>\n" );
document.write( "y-intercept: set x=0 and evaluate.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%280-1%29%5E2-50 ALIGN=MIDDLE  ALT=\"y+=+2%280-1%29%5E2-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2-50+=+-48 ALIGN=MIDDLE  ALT=\"y+=+2-50+=+-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The y-intercept is -48, or (0,-48).<br><BR>\n" );
document.write( "3) roots -3 and 7; coefficient a is -1/5<br><BR>\n" );
document.write( "This one is nearly done for you:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F5%29%28x%2B3%29%28x-7%29 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F5%29%28x%2B3%29%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "maximum value: by the symmetry of a parabola, the maximum value is at the x value halfway between the roots, at x=2.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1%2F5%29%282%2B3%29%282-7%29+=+%28-1%29%28-5%29+=+5 ALIGN=MIDDLE  ALT=\"y+=+%28-1%2F5%29%282%2B3%29%282-7%29+=+%28-1%29%28-5%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The maximum value is 5. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );