document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=638113>Question 638113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the x-intercepts of the parabola with vertex (4,75)and y-intercept(o,27). Write your answer in this form: (x1,y1),(x2,y2). If necessary, round to the nearest hundredth.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #402038 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=402038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given a parabolic function<BR>\n" );
document.write( "(1) y = ax^2 + bx +c, <BR>\n" );
document.write( "that passes through (0,27) and has a vertex at (4,75).<BR>\n" );
document.write( "When x = 0 we have<BR>\n" );
document.write( "y = c, therefore <BR>\n" );
document.write( "(2) c = 27<BR>\n" );
document.write( "The vertex value of x is equal to 4. Using the formula<BR>\n" );
document.write( "x = -b/(2a), we get<BR>\n" );
document.write( "-b/(2a) = 4 or<BR>\n" );
document.write( "(3) b = -8a<BR>\n" );
document.write( "Substituting (2) and (3) into (1) yields<BR>\n" );
document.write( "(4) y = ax^2 -8ax + 27<BR>\n" );
document.write( "Using the vertex point (4,75) we obtain<BR>\n" );
document.write( "a4^2 - 8a(4) + 27 = 75 which simplifies to<BR>\n" );
document.write( "16a - 32a = 75-27 or<BR>\n" );
document.write( "-16a = 48<BR>\n" );
document.write( "(5) a = -3<BR>\n" );
document.write( "Substitute a into (3) yields<BR>\n" );
document.write( "(6) b = 24<BR>\n" );
document.write( "The parabola is<BR>\n" );
document.write( "(7) y = -3x^2 + 24x + 27<BR>\n" );
document.write( "To check (7), put in (4,75)<BR>\n" );
document.write( "Is (75 = -3*16 + 96 + 27)?<BR>\n" );
document.write( "Is (75 = -48 + 123)?<BR>\n" );
document.write( "Is (75 = 75)? Yes<BR>\n" );
document.write( "To find the values of x that make y = 0, set (7) to zero<BR>\n" );
document.write( "y = -3x^2 +24x +27 <BR>\n" );
document.write( "y = -3(x^2-8x-9) = 0 or<BR>\n" );
document.write( "(x^2 -8x -9) = 0<BR>\n" );
document.write( "Factoring y yields<BR>\n" );
document.write( "(8) (x-9)(x+1) = 0<BR>\n" );
document.write( "Which gives the roots, x = {-1,9}<BR>\n" );
document.write( "Check these values by substitution into (7)<BR>\n" );
document.write( "Is [0 = -3(-1)^2 +24(-1)+27]?<BR>\n" );
document.write( "Is [0 = -3 -24 +27]?<BR>\n" );
document.write( "Is [0 = 0]? Yes<BR>\n" );
document.write( "Is [0 = -3(9)^2 +24*9+27]?<BR>\n" );
document.write( "Is [0 = -243 +216 + 27]?<BR>\n" );
document.write( "Is [0 = 0]? Yes<BR>\n" );
document.write( "Answer: The x intercepts are {(-1,0),(9,0)} </SPAN>\n" );
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