document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178347>Question 1178347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7. The path of a baseball after it is hit is modelled by the equation h=-4.98t^2+12.51t+1.36, where h is the height, in metres, of the ball and t is the time, in seconds, after the ball is hit.\r<BR>\n" );
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document.write( "a. Find the maximum height that the ball reaches, to the nearest hundredth of a metre.\r<BR>\n" );
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document.write( "b. Determine the height of the ball, to the nearest hundredth of a metre, at 2.5 seconds.\r<BR>\n" );
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document.write( "c. Determine when the ball is at a height of 8m, to the nearest hundredth of a second. (2 marks)\r<BR>\n" );
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document.write( "d. State the y-intercept of the graph to the nearest hundredth. Describe what the y-intercept represents in the context of this question.\r<BR>\n" );
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document.write( "e.i. Find the coordinates of both x-intercepts of the graph to the nearest hundredth.\r<BR>\n" );
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document.write( "ii. State what the positive x-intercept represents in the context of this problem.\r<BR>\n" );
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document.write( "iii. Explain why the negative x-intercept is not valid in the context of this problem.<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 #807577 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( " 7. The path of a baseball after it is hit is modelled by the equation\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.98t%5E2%2B12.51t%2B1.36 ALIGN=MIDDLE  ALT=\"h=-4.98t%5E2%2B12.51t%2B1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height, in metres, of the ball and<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t ALIGN=MIDDLE  ALT=\"+t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the time, in seconds, after the ball is hit.\r<BR>\n" );
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document.write( "a. Find the maximum height that the ball reaches, to the nearest hundredth of a metre.<BR>\n" );
document.write( "You have to take the derivative of the function and set it equal to<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0 ALIGN=MIDDLE  ALT=\"+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  That's where the ball would reach it's top point.  So the derivative is  <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.98t%2B12.51+=+0 ALIGN=MIDDLE  ALT=\"-4.98t%2B12.51+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........solve this equation for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.51+=+4.98t ALIGN=MIDDLE  ALT=\"12.51+=+4.98t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.51%2F+4.98=+t ALIGN=MIDDLE  ALT=\"12.51%2F+4.98=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.51 ALIGN=MIDDLE  ALT=\"t=2.51\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute this value of t into the original equation to get the maximum height.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.98%282.512%29%5E2%2B12.51%282.512%29%2B1.36 ALIGN=MIDDLE  ALT=\"h=-4.98%282.512%29%5E2%2B12.51%282.512%29%2B1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1.36 ALIGN=MIDDLE  ALT=\"h=1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Determine the height of the ball, to the nearest hundredth of a metre, at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5 ALIGN=MIDDLE  ALT=\"2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4.98%282.5%29%5E2%2B12.51%282.5%29%2B1.36 ALIGN=MIDDLE  ALT=\"h=-4.98%282.5%29%5E2%2B12.51%282.5%29%2B1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1.51 ALIGN=MIDDLE  ALT=\"h=1.51\"   DISABLED_style= \"max-width:90%; height:auto;\" >m\r<BR>\n" );
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document.write( "c. Determine when the ball is at a height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8m ALIGN=MIDDLE  ALT=\"8m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to the nearest hundredth of a second. (2 marks)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=-4.98t%5E2%2B12.51t%2B1.36 ALIGN=MIDDLE  ALT=\"8=-4.98t%5E2%2B12.51t%2B1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-4.98t%5E2%2B12.51t%2B1.36-8 ALIGN=MIDDLE  ALT=\"0=-4.98t%5E2%2B12.51t%2B1.36-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-4.98t%5E2%2B12.51t-6.64 ALIGN=MIDDLE  ALT=\"0=-4.98t%5E2%2B12.51t-6.64\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........using the quadratic formula we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0.76 ALIGN=MIDDLE  ALT=\"t=0.76\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t=1.75 ALIGN=MIDDLE  ALT=\"+t=1.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds\r<BR>\n" );
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document.write( "d. State the y-intercept of the graph to the nearest hundredth. Describe what the y-intercept represents in the context of this question.\r<BR>\n" );
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document.write( "The y-intercept occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the equation.  You get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.36 ALIGN=MIDDLE  ALT=\"1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  What that means is that the ball STARTS at a height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.36 ALIGN=MIDDLE  ALT=\"1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters, which would be the height of the bat when it hits the ball.\r<BR>\n" );
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document.write( "y-intercept is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.36 ALIGN=MIDDLE  ALT=\"1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "e.i. Find the coordinates of both x-intercepts of the graph to the nearest hundredth.\r<BR>\n" );
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document.write( "set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-4.98t%5E2%2B12.51t%2B1.36 ALIGN=MIDDLE  ALT=\"0=-4.98t%5E2%2B12.51t%2B1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........using the quadratic formula we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-0.10 ALIGN=MIDDLE  ALT=\"t=-0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.62 ALIGN=MIDDLE  ALT=\"t=2.62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x-intercept is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.10 ALIGN=MIDDLE  ALT=\"-0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.62 ALIGN=MIDDLE  ALT=\"2.62\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "ii. State what the positive x-intercept represents in the context of this problem.\r<BR>\n" );
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document.write( "Time the ball hits the ground  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.62 ALIGN=MIDDLE  ALT=\"2.62\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds after being hit.\r<BR>\n" );
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document.write( "iii. Explain why the negative x-intercept is not valid in the context of this problem.\r<BR>\n" );
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document.write( "The ball is starting from a height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.36 ALIGN=MIDDLE  ALT=\"1.36\"   DISABLED_style= \"max-width:90%; height:auto;\" > m at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Where it was before being hit is non-sequitur.<BR>\n" );
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