document.write( "Question 128351: Given the parabola y=x^2-6x-7, answer the following questions:
\n" ); document.write( "what is its x-intercept? Find its y-intercept. Graph the parabola. \n" ); document.write( "

Algebra.Com's Answer #93958 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First let's find the x-intercept(s)\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "To find the x-intercept, let y=0\r
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\n" ); document.write( "\n" ); document.write( " $\"0=x%5E2-6x-7\"$ Plug in $\"y=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"0=%28x-7%29%28x%2B1%29\"$ Factor the right side (note: if you need help with factoring, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
\n" ); document.write( "\n" ); document.write( " $\"x-7=0\"$ or $\"x%2B1=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=7\"$ or $\"x=-1\"$ Now solve for x in each case\r
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\n" ); document.write( "\n" ); document.write( "So the x-intercepts are (-1,0) and (7,0)\r
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\n" ); document.write( "\n" ); document.write( "Now let's find the y-intercept\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "To find the y-intercept, let x=0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1%280%29%5E2-6%280%29-7\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=1%2A0-6%2A0-7\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0-6%2A0-7\"$ Multiply 1 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0-0-7\"$ Multiply 6 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0-7\"$ Subtract 0 from 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-7\"$ Subtract 7 from 0 to get -7\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the y-intercept is (0,-7)\r
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\n" ); document.write( "\n" ); document.write( "If we graph the parabola, we get\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-6x-7%29+\"$ Graph of $\"y=x%5E2-6x-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "We can see that the x-intercepts are (-1,0) and (7,0) and that the y-intercept is (0,-7). So this verifies our answer. \n" ); document.write( "

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