document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198798>Question 1198798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6. Determine the equation in vertex form for the following equation.	<BR>\n" );
document.write( "Vertex = (-1,6)<BR>\n" );
document.write( "Points = (0,4)	\r<BR>\n" );
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document.write( "7. Graph the equation in Desmos or Geogebra. Then answer the following questions. A person throws a ball straight up in the air. The height of a ball, h, in meters, can be modelled by h=-4.9t2+10.78t+1.071, where t is the time in seconds since the ball was thrown.\r<BR>\n" );
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document.write( "a) What is the maximum height the ball can reach?	<BR>\n" );
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document.write( "b) How tall is the person that throws the ball up in the air?			\r<BR>\n" );
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document.write( "c) If the thrower also wants to catch the ball, what time do you think that will occur at? <BR>\n" );
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document.write( "d) What is an appropriate domain and range for this situation? Explain why you chose these parameters.									<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 #837991 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor uses the given vertex and the given other point, along with the vertex form of the equation, to determine the coefficient \"a\":<br><BR>\n" );
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document.write( "we use the vertex form equation.\r<BR>\n" );
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document.write( "f(x) = a(x - h)^2 + k\r<BR>\n" );
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document.write( "where (h, k) represents the coordinates of the vertex.\r<BR>\n" );
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document.write( "Given the vertex (-1, 6), we substitute the values into the equation:\r<BR>\n" );
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document.write( "f(x) = a(x - (-1))^2 + 6\r<BR>\n" );
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document.write( "Simplifying further:\r<BR>\n" );
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document.write( "f(x) = a(x + 1)^2 + 6\r<BR>\n" );
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document.write( " using the given point (0, 4).\r<BR>\n" );
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document.write( "Substitute x and f(x) into the equation:\r<BR>\n" );
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document.write( "4 = a(0 + 1)^2 + 6\r<BR>\n" );
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document.write( "4 = a(1)^2 + 6\r<BR>\n" );
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document.write( "4 = a + 6\r<BR>\n" );
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document.write( "a = -2\r<BR>\n" );
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document.write( "------------------------------------------------------------------------<br><BR>\n" );
document.write( "If you have a good understanding of the vertex form of the equation of a parabola, then you can find the coefficient \"a\" with much less work using this shortcut.<br><BR>\n" );
document.write( "The other given point is 1 unit to the right of the vertex. The value 1 unit to the right of the vertex will differ from the value at the vertex by a(1^2) = a.  Since the value at the other point is 2 less than the value at the vertex, the coefficient \"a\" is -2.<br><BR>\n" );
document.write( "Once you have found the value of \"a\", then continue as the other tutor does to find the equation in vertex form is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-6=-2%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"y-6=-2%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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