document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206459>Question 1206459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function h(t)=-16t^2+16t represents the height (in feet) of a horse t seconds after it jumps over a pole.When does the horse reach its maximum height </SPAN>\n" );
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document.write( "Answer: <font color=red>0.5 seconds</font>\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "I'll use x in place of t.\r<BR>\n" );
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document.write( "The equation we consider is<BR>\n" );
document.write( "y = -16x^2+16x\r<BR>\n" );
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document.write( "Plug in y = 0 to find the x intercepts.<BR>\n" );
document.write( "-16x^2+16x = 0<BR>\n" );
document.write( "-16x(x - 1) = 0<BR>\n" );
document.write( "-16x = 0 or x-1 = 0<BR>\n" );
document.write( "x = 0 or x = 1\r<BR>\n" );
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document.write( "The parabola opens downward since the leading coefficient (-16) is negative.<BR>\n" );
document.write( "The x intercepts are x = 0 and x = 1. <BR>\n" );
document.write( "Due to symmetry, the x coordinate of the max height occurs at the midpoint of those roots.\r<BR>\n" );
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document.write( "Add up the x intercept values and divide in half<BR>\n" );
document.write( "(a+b)/2 = (0+1)/2 = 1/2 = <font color=red>0.5</font><BR>\n" );
document.write( "The max height occurs when x = <font color=red>0.5</font><BR>\n" );
document.write( "This is the final answer since your teacher wants the time value when this max height occurs.\r<BR>\n" );
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document.write( "Another way to find this value is to use the formula: h = -b/(2a) <BR>\n" );
document.write( "h = x coordinate of vertex<BR>\n" );
document.write( "a,b are the first two coefficients of the function. <BR>\n" );
document.write( "In this case a = -16 and b = 16.\r<BR>\n" );
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document.write( "To find the max height itself, plug x = 0.5 into the function to find:<BR>\n" );
document.write( "y = -16x^2+16x <BR>\n" );
document.write( "y = -16(0.5)^2+16(0.5) <BR>\n" );
document.write( "y = 4<BR>\n" );
document.write( "The point (0.5, 4) is the highest point on the parabola.\r<BR>\n" );
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document.write( "The horse reaches the max height of 4 feet at the time 0.5 seconds.<BR>\n" );
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