document.write( "Question 77254: the graph of the equation y=x^2+2x-8 where does it intersect the x-axis? \n" ); document.write( "
Algebra.Com's Answer #55473 by jim_thompson5910(35256)\"\" \"About 
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To find the x-intercepts, we need to factor \"x%5E2%2B2x-8\"\r
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Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B2%2Ax%2B-8\", first we need to ask ourselves: What two numbers multiply to -8 and add to 2? Lets find out by listing all of the possible factors of -8
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1,2,4,8,
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\n" ); document.write( " -1,-2,-4,-8,List the negative factors as well. This will allow us to find all possible combinations
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\n" ); document.write( " These factors pair up to multiply to -8.
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\n" ); document.write( " (-1)*(8)=-8
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\n" ); document.write( " (-2)*(4)=-8
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\n" ); document.write( " Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
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First Number|Second Number|Sum
1|-8|1+(-8)=-7
2|-4|2+(-4)=-2
-1|8|(-1)+8=7
-2|4|(-2)+4=2
We can see from the table that -2 and 4 add to 2.So the two numbers that multiply to -8 and add to 2 are: -2 and 4\r\n" ); document.write( " \r\n" ); document.write( " Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" ); document.write( " \r\n" ); document.write( " \"%28x%2Ba%29%28x%2Bb%29\"substitute a=-2 and b=4\r\n" ); document.write( " \r\n" ); document.write( " So the equation becomes:\r\n" ); document.write( " \r\n" ); document.write( " (x-2)(x+4)\r\n" ); document.write( " \r\n" ); document.write( " Notice that if we foil (x-2)(x+4) we get the quadratic \"1%2Ax%5E2%2B2%2Ax%2B-8\" again\n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "So the equation becomes\r
\n" ); document.write( "\n" ); document.write( "\"y=%28x-2%29%28x%2B4%29\"\r
\n" ); document.write( "\n" ); document.write( "Now let y=0\r
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\n" ); document.write( "\n" ); document.write( "\"0=%28x-2%29%28x%2B4%29\"\r
\n" ); document.write( "\n" ); document.write( "Set each factor equal to zero:\r
\n" ); document.write( "\n" ); document.write( "\"x-2=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x=2\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B4=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x=-4\"\r
\n" ); document.write( "\n" ); document.write( "So the solutions are:\r
\n" ); document.write( "\n" ); document.write( "\"x=2\" or \"x=-4\"\r
\n" ); document.write( "\n" ); document.write( "which means the x-intercepts are:\r
\n" ); document.write( "\n" ); document.write( "(2,0) and (-4,0)\r
\n" ); document.write( "\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2Cx%5E2%2B2x-8%29+\" graph of \"y=x%5E2%2B2x-8\"
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