document.write( "Question 312383: Please help! I am lost in how to figure this out:\r
\n" ); document.write( "\n" ); document.write( "f(x)= -2x^2+2x+8\r
\n" ); document.write( "\n" ); document.write( "This one has several parts..\r
\n" ); document.write( "\n" ); document.write( "The x coordinate of the vertex?\r
\n" ); document.write( "\n" ); document.write( "The y coordinate of the vertex?\r
\n" ); document.write( "\n" ); document.write( "The equation of the line of symmetry?\r
\n" ); document.write( "\n" ); document.write( "The maximum/minimum of f(x)?\r
\n" ); document.write( "\n" ); document.write( "Is the value of f(1/2)=17/2 maximum or minimum?\r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #223301 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
Please help! I am lost in how to figure this out:\r
\n" ); document.write( "\n" ); document.write( " $\"%22f%28x%29%22=+-2x%5E2%2B2x%2B8\"$
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document.write( "That's the same as\r\n" );
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document.write( "Plot some points:\r\n" );
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document.write( "(-2,-4), (-1,4), (0,8), (1,8), (2,4), (3,-4)\r\n" );
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document.write( "and get this graph:\r\n" );
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\n" ); document.write( "This one has several parts..\r
\n" ); document.write( "\n" ); document.write( "The x coordinate of the vertex?
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document.write( "Learn the formula:\r\n" );
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document.write( "The x-coordinate of  is \r\n" );
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document.write( "Compare\r\n" );
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document.write( "to\r\n" );
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document.write( "and observe that , , \r\n" );
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document.write( "Then substitute and get\r\n" );
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\n" ); document.write( "The y coordinate of the vertex?
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document.write( "Learn the rule: To get the y-coordinate of the vertex,\r\n" );
document.write( "after finding the x-coordinate of the vertex, substitute\r\n" );
document.write( "the value of the x-coordinate of the vertex x in the original \r\n" );
document.write( "equation:\r\n" );
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document.write( "So the y coordinate of the vertex is  or \r\n" );
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document.write( "That makes the vertes (,), or (0.5,8.5)\r\n" );
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document.write( "and we see that looks right according to the graph:\r\n" );
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\n" ); document.write( "The equation of the line of symmetry?
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document.write( "Learn the rule that the equation of the line of symmetry\r\n" );
document.write( "is always the vertical line whose equation is\r\n" );
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document.write( "x = the x-coordinate of the vertex\r\n" );
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document.write( "So the axis of symmetry has the equation \r\n" );
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document.write( " or \r\n" );
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document.write( "which is a vertical line  a unit right of the y-axis\r\n" );
document.write( "and parallel to it (vertical), and when we graph it (in green,\r\n" );
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document.write( "and we see that this vertical line whose equation is ,\r\n" );
document.write( "bisects the parabola. \r\n" );
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\n" ); document.write( "The maximum/minimum of f(x)?
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document.write( "Learn that the maximum or minimum value is the y-coordinate of\r\n" );
document.write( "the vertex.\r\n" );
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document.write( "The maximum or minimum point is the same as the vertex.\r\n" );
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document.write( "To determine whether or not it is a maximum or a minimum\r\n" );
document.write( "we need to know whether the parabola opens upward or downward.\r\n" );
document.write( "To determine this we look at the coefficient of .\r\n" );
document.write( "If it is positive then the parabola opens upward and the\r\n" );
document.write( "vertex is a minimum point. If it is negative, the parabola \r\n" );
document.write( "opens downward and the vertex is a maximum.  \r\n" );
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document.write( "Here we see that the coefficient of  is negative and\r\n" );
document.write( "that the parabola opens downward, so the vertex is a maximum.\r\n" );
document.write( "We knew it opened downward because we graphed it, but we\r\n" );
document.write( "would have known it opened downward even if we had not\r\n" );
document.write( "graphed it because the coefficient of  is negative. \r\n" );
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\n" ); document.write( "Is the value of $\"f%281%2F2%29=17%2F2\"$ maximum or minimum?
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document.write( "It is a maximum as we have just seen.\r
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document.write( "Thanks! \n" );
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