document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=402729>Question 402729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I am having a hard time with the following two problems. Could someone please help with them I would very much appreciate it! Thanks\r<BR>\n" );
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document.write( " Consider the parabola with equation f(x)= -x^2-2x+15<BR>\n" );
document.write( "(a) Does the parabola open up or down?<BR>\n" );
document.write( "(b) What is the equation for the axis of symmetry for the parabola?<BR>\n" );
document.write( "(c) What are the coordinates of the vertex of the parabola?<BR>\n" );
document.write( "(d) What is the y-intercept of the parabola?<BR>\n" );
document.write( "(e) Determine the x-intercepts if there are any.<BR>\n" );
document.write( "(f) Sketch a graph of the parabola.\r<BR>\n" );
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document.write( " A parabola has an x-intercept at 2, its axis of symmetry is the line x = 4, and the y- coordinate of its vertex is 6. Determine the equation of the parabola. Hint: The equation looks like y = ax^2+bx+c. Use the given information to figure out what a, b, c must be. For example, when x = 2, the y value must be 0 since 2 is an x-intercept. That means 0 = 4a + 2b + c. The other two given facts provide similar information about a, b, c. \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 #284888 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=284888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the parabola with equation f(x)= -x^2-2x+15<BR>\n" );
document.write( "(a) Does the parabola open up or down?<BR>\n" );
document.write( "Down, the x^2 term is negative.<BR>\n" );
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document.write( "(b) What is the equation for the axis of symmetry for the parabola?<BR>\n" );
document.write( "x = -b/2a = 2/(-2)<BR>\n" );
document.write( "x = -1<BR>\n" );
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document.write( "(c) What are the coordinates of the vertex of the parabola?<BR>\n" );
document.write( "It's (x,f(x)) on the line of symmetry.<BR>\n" );
document.write( "f(-1) = 16<BR>\n" );
document.write( "--> (-1,16)<BR>\n" );
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document.write( "(d) What is the y-intercept of the parabola?<BR>\n" );
document.write( "f(0) = 15 or (0,15)<BR>\n" );
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document.write( "(e) Determine the x-intercepts if there are any.<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B-2x%2B15+=+0 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-2x%2B15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-2%29%5E2-4%2A-1%2A15=64 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A-1%2A15=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=64 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2%2B-sqrt%28+64+%29%29%2F2%5Ca\"   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%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C-1+=+-5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+64+%29%29%2F2%5C-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%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C-1+=+3 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2%29-sqrt%28+64+%29%29%2F2%5C-1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B-2x%2B15 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-2x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B-2x%2B15+=+%28x--5%29%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B-2x%2B15+=+%28x--5%29%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -5, 3.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-2%2Ax%2B15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "(f) Sketch a graph of the parabola.<BR>\n" );
document.write( "dl the FREE graph software at<BR>\n" );
document.write( "http://www.padowan.dk </SPAN>\n" );
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