document.write( "Question 90223This question is from textbook Beginning Algebra
\n" ); document.write( ": I need to identify the axis of symmetry, create a suitable table of values and sketch a graph including the axis of symmetry for: y = x^2 - 5x +3\r
\n" ); document.write( "\n" ); document.write( "I know the formula to find the axis is x = -b/2a thus
\n" ); document.write( "x = -(-5)/2(1) = 5/2\r
\n" ); document.write( "\n" ); document.write( "From here on out I'm lost. I get really confused whenever fractions are involved. I'm not sure what numbers to choose for my values and why to choose those numbers.\r
\n" ); document.write( "\n" ); document.write( "Any help would be appreciate. \n" ); document.write( "

Algebra.Com's Answer #65473 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Since you know the x-value of the vertex (which is $\"5%2F2\"$ ) plug in $\"x=5%2F2\"$ to find the y value\r
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\n" ); document.write( "\n" ); document.write( " $\"y+=+%285%2F2%29%5E2+-+5%285%2F2%29+%2B3+\"$ plug in $\"x=5%2F2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y+=+25%2F4+-+25%2F2+%2B3+\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y+=+25%2F4+-+50%2F4+%2B12%2F4+\"$ Make into equivalent fractions with the common denominator\r
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\n" ); document.write( "\n" ); document.write( " $\"y+=+%2825-50%2B12%29%2F4+\"$ Combine the fractions\r
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\n" ); document.write( "\n" ); document.write( " $\"y+=+-13%2F4+\"$ combine the numerator\r
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\n" ); document.write( "\n" ); document.write( "So the vertex is ( $\"5%2F2\"$ , $\"-13%2F4\"$ ) which is one point on our graph\r
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\n" ); document.write( "\n" ); document.write( "Now plug in the x-values $\"x=1\"$ , $\"x=2\"$ , $\"x=3\"$ , $\"x=4\"$ (notice x=1 and x=4 are the same distance from x=2.5, which is the axis of symmetry. Also x=2 and x=3 are the same distance from x=2.5.)\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%281%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B3\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29%5E2-5%281%29%2B3\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29-5%281%29%2B3\"$ Raise 1 to the second power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=%281%29-5%2B3\"$ Multiply 5 by 1 to get 5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (1,-1)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%282%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B3\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%282%29%5E2-5%282%29%2B3\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%284%29-5%282%29%2B3\"$ Raise 2 to the second power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=%284%29-10%2B3\"$ Multiply 5 by 2 to get 10\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (2,-3)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%283%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B3\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%283%29%5E2-5%283%29%2B3\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%289%29-5%283%29%2B3\"$ Raise 3 to the second power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=%289%29-15%2B3\"$ Multiply 5 by 3 to get 15\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-3\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (3,-3)\r
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\n" ); document.write( "\n" ); document.write( "----Now lets find another point----\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Lets evaluate $\"f%284%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2-5x%2B3\"$ Start with the given polynomial\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%284%29%5E2-5%284%29%2B3\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%2816%29-5%284%29%2B3\"$ Raise 4 to the second power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=%2816%29-20%2B3\"$ Multiply 5 by 4 to get 20\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-1\"$ Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (4,-1)\r
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\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated (note: I'm writing $\"5%2F2\"$ as 2.5 and $\"-13%2F4\"$ as -3.25)\r
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document.write( " x y
 1 -1
 2 -3
 2.5 -3.25
 3 -3
 4 -1\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice how the x-values x=1 and x=2 have the same y value as x=3 and x=4. So to save time, you only need half of these points to make an adequate table (since the parabola is symmetrical)\r
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\n" ); document.write( "\n" ); document.write( "Here you can see that the parabola is symmetrical about the axis of symmetry\r
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