document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596109>Question 596109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am in my last few weeks of my algebra class and it is getting really hard for me can someone please help me solve these problems?<BR>\n" );
document.write( "1. For the first part of this worksheet, we’ll be looking at the equation<BR>\n" );
document.write( "y = -16x² + 368x + 144<BR>\n" );
document.write( "(a) +Does the graph of this equation open up or down? How do you know?<BR>\n" );
document.write( "(b) Describe the shape of the graph.<BR>\n" );
document.write( "(c) Will the graph of y = -16x² + 368x + 144 reach a maximum or a minimum?<BR>\n" );
document.write( "(d) Find the x-coordinate of the vertex. Show your work!<BR>\n" );
document.write( "(e) Find the y-coordinate of the vertex. Show your work!<BR>\n" );
document.write( "(f) Find the discriminant for the equation -16t2 + 368t + 144 = 0<BR>\n" );
document.write( "(g) How many solutions are there to the equation from part (f)? How do you know?<BR>\n" );
document.write( "NOTE: You will find the solution(s) in part (h). In this part, you are just supposed to think about how many solutions there will be without finding the solutions first.<BR>\n" );
document.write( "(h) Use the quadratic formula to determine solution(s) to the equation in (f). Give the exact solutions, in simplified form. Show your work!<BR>\n" );
document.write( "(i) Find the decimal approximations for the solutions you found in (h).\r<BR>\n" );
document.write( "\n" );
document.write( "My answers:<BR>\n" );
document.write( "(a) The graph would open up because the equation is positive.<BR>\n" );
document.write( "(b) The graph would be U shaped.<BR>\n" );
document.write( "(c) Maximum </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377528 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. For the first part of this worksheet, we’ll be looking at the equation<BR>\n" );
document.write( "y = -16x² + 368x + 144<BR>\n" );
document.write( "(a) +Does the graph of this equation open up or down? How do you know?<BR>\n" );
document.write( "The coefficient of the x^2 term is negative, so it opens downward.<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(b) Describe the shape of the graph.<BR>\n" );
document.write( "It's a parabola.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "(c) Will the graph of y = -16x² + 368x + 144 reach a maximum or a minimum?<BR>\n" );
document.write( "It has a max, due to part (a).<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "(d) Find the x-coordinate of the vertex.<BR>\n" );
document.write( "The LOS (Line of Symmetry) is x = -b/2a<BR>\n" );
document.write( "x = -368/-32<BR>\n" );
document.write( "x = 11.5<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(e) Find the y-coordinate of the vertex.<BR>\n" );
document.write( "f(11.5) = -16*11.5^2 + 368*11.5 + 144<BR>\n" );
document.write( "= 2260<BR>\n" );
document.write( "(f) Find the discriminant for the equation -16t2 + 368t + 144 = 0<BR>\n" );
document.write( "Disc = b^2 - 4ac = 368^2 -4*-16(144)<BR>\n" );
document.write( "Disc = 144640<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(g) How many solutions are there to the equation from part (f)?<BR>\n" );
document.write( "The Disc > 0 --> 2 real solutions.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "(h) Use the quadratic formula to determine solution(s) to the equation in (f). Give the exact solutions, in simplified form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-368%2F-32+%2B-+sqrt%28Disc%29%2F-32 ALIGN=MIDDLE  ALT=\"x+=+-368%2F-32+%2B-+sqrt%28Disc%29%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+11.5+%2B-+sqrt%28565%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+11.5+%2B-+sqrt%28565%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(i) Find the decimal approximations for the solutions you found in (h).<BR>\n" );
document.write( "x = 23.385<BR>\n" );
document.write( "x = -0.385<BR>\n" );
document.write( "========================================<BR>\n" );
document.write( "My answers:<BR>\n" );
document.write( "(a) The graph would open up because the equation is positive.<BR>\n" );
document.write( "(b) The graph would be U shaped.<BR>\n" );
document.write( "(c) Maximum </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );