document.write( "Question 968090: Y=x^2+2x-3
\n" ); document.write( "Y=2x+1\r
\n" ); document.write( "\n" ); document.write( "Need help with this question please\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #591666 by KMST(5328) $\"\"$ $\"About$

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$\"y=2x%2B1\"$ is a linear equation. Its graph is a straight line.
\n" ); document.write( " $\"y=x%5E2%2B2x-3\"$ is not a linear equation.
\n" ); document.write( "It is an equation of degree 2 (the greatest exponent),
\n" ); document.write( "and we call it a quadratic equation.
\n" ); document.write( "Quadratic functions like $\"y=x%5E2%2B2x-3\"$ graph as parabolas,
\n" ); document.write( "and this one looks like $\"graph%28300%2C500%2C-6%2C6%2C-5%2C15%2Cx%5E2%2B2x-3%29\"$ .
\n" ); document.write( "The two function graphed together look like this:
\n" ); document.write( " $\"graph%28300%2C500%2C-6%2C6%2C-5%2C15%2Cx%5E2%2B2x-3%2C2x%2B1%29\"$ .
\n" ); document.write( "It is easy to see that there will be two answers:
\n" ); document.write( "the two pairs of coordinates of the intersection points.
\n" ); document.write( "Let's find them.
\n" ); document.write( "There are, and there will be two equations,
\n" ); document.write( "but we can combine them so as to get an equation with no $\"y\"$ ,
\n" ); document.write( "and replace the combination for one of the equations,
\n" ); document.write( "We can easily combine them by substituting
\n" ); document.write( "the expression $\"2x%2B1\"$ for $\"y\"$
\n" ); document.write( "in the equation that is not $\"y=2x%2B1\"$ .
\n" ); document.write( "We can keep the simpler equation $\"y=2x%2B1\"$ ,
\n" ); document.write( "and substitute the combination for the other one.
\n" ); document.write( " $\"system%28y=2x%2B1%2Cy=x%5E2%2B2x-3%29\"$ ---> $\"system%28y=2x%2B1%2C2x%2B1=x%5E2%2B2x-3%29\"$
\n" ); document.write( "Now we solve the equation in $\"x\"$ (no $\"y\"$ )
\n" ); document.write( " $\"2x%2B1=x%5E2%2B2x-3\"$
\n" ); document.write( " $\"2x%2B1-2x-1=x%5E2%2B2x-3-2x-1\"$
\n" ); document.write( " $\"0=x%5E2-4\"$
\n" ); document.write( " $\"0%2B4=x%5E2-4%2B4\"$
\n" ); document.write( " $\"4=x%5E2\"$
\n" ); document.write( "There are two solutions for $\"x\"$ : $\"system%28x=2%2C%22or%22%2Cx=-2%29\"$ ,
\n" ); document.write( "and for each of them, there will be a corresponding $\"y%7D%7D+value%2C+given+by+%7B%7B%7By=2x%2B1\"$ .
\n" ); document.write( "For $\"x=2\"$ :
\n" ); document.write( " $\"system%28y=2x%2B1%2Cx=2%29\"$ --> $\"system%28y=2%2A2%2B1%2Cx=2%29\"$ --> $\"system%28y=4%2B1%2Cx=2%29\"$ --> $\"highlight%28system%28y=5%2Cx=2%29%29\"$
\n" ); document.write( "For $\"x=-2\"$ :
\n" ); document.write( " $\"system%28y=2x%2B1%2Cx=2%29\"$ --> $\"system%28y=2%2A%28-2%29%2B1%2Cx=2%29\"$ --> $\"system%28y=-4%2B1%2Cx=2%29\"$ --> $\"highlight%28system%28y=-3%2Cx=2%29%29\"$ \n" ); document.write( "

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