document.write( "Question 114163: Find the x- and y- intercepts for the quadratic equation y = x^2 + 6x + 8 \n" ); document.write( "

Algebra.Com's Answer #83082 by bucky(2189) $\"\"$ $\"About$

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To get the point on the y axis where the graph crosses, set the value of x at zero and solve
\n" ); document.write( "the equation for the corresponding value of y. [Note that for any point on the y-axis the
\n" ); document.write( "value of x for that point is zero.] So to find the value of the y-intercept, you go to the
\n" ); document.write( "equation:
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\n" ); document.write( " $\"y+=+x%5E2+%2B+6x+%2B+8\"$
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\n" ); document.write( "and set x = 0 to get that:
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\n" ); document.write( " $\"y+=+0%5E2+%2B+6%2A0+%2B+8\"$
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\n" ); document.write( "The first two terms on the right side equal zero so the equation reduces to:
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\n" ); document.write( " $\"y+=+8\"$
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\n" ); document.write( "This means the graph crosses the y-axis at +8 on the y-axis.
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\n" ); document.write( "Similarly you can find the values where the graph crosses the x-axis by setting y equal to zero
\n" ); document.write( "because any coordinate point on the x-axis has zero for its y value. Setting y equal to zero
\n" ); document.write( "in the equation leads to:
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\n" ); document.write( " $\"0+=+x%5E2+%2B+6x+%2B+8\"$
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\n" ); document.write( "and transposing this equation (switching sides just to get it into a little more familiar
\n" ); document.write( "format) results in:
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\n" ); document.write( " $\"x%5E2+%2B+6x+%2B+8+=+0\"$
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\n" ); document.write( "Notice that the left side can be factored to convert the equation to:
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\n" ); document.write( " $\"%28x+%2B+4%29%28x+%2B+2%29+=+0\"$
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\n" ); document.write( "[You can multiply out the left side, just to make sure we factored it correctly, if you would
\n" ); document.write( "like to.]
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\n" ); document.write( "This factored form will be correct if either of the factors is equal to zero, because if
\n" ); document.write( "either factor is zero, the left side will involve a multiplication by zero ... and this
\n" ); document.write( "makes the entire left side equal to zero and therefore equal to the right side.
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\n" ); document.write( "So set each of the factors equal to zero. First:
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\n" ); document.write( " $\"x+%2B+4+=+0\"$
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\n" ); document.write( "which, by subtracting 4 from both sides, becomes:
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\n" ); document.write( " $\"x+=+-4\"$
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\n" ); document.write( "Then, set:
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\n" ); document.write( " $\"x+%2B+2+=+0\"$
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\n" ); document.write( "which, by subtracting 2 from both sides, becomes:
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\n" ); document.write( " $\"x+=+-2\"$
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\n" ); document.write( "This tells us that the x-axis intercepts cross the x-axis at -4 and -2.
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\n" ); document.write( "The graph for the original equation is:
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\n" ); document.write( " $\"graph%28600%2C600%2C-15%2C15%2C-15%2C15%2Cx%5E2%2B6x%2B8%29\"$
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\n" ); document.write( "Notice where the x and y axis intercepts are. They match the work that we did.
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\n" ); document.write( "Hope this helps you to understand the problem and how to get the answers.
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