document.write( "Question 1118926: y=1/2x^2+x-4 \r
\n" ); document.write( "\n" ); document.write( " Sketch the following quadratic relationship by finding the x-intercepts , the y intercept, axis of symmetry, mirror of the y intercept and the vertex \n" ); document.write( "

Algebra.Com's Answer #734345 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"y=%281%2F2%29x%5E2%2Bx-4\"$

\n" ); document.write( "Factor out the leading coefficient and complete the square in x to find the vertex and axis of symmetry.

\n" ); document.write( " $\"y+=+%281%2F2%29%28x%5E2%2B2x-8%29\"$
\n" ); document.write( " $\"y+=+%281%2F2%29%28x%5E2%2B2x%2B1-9%29\"$
\n" ); document.write( " $\"y+=+%281%2F2%29%28%28x%5E2%2B2x%2B1%29-9%29\"$
\n" ); document.write( " $\"y+=+%281%2F2%29%28%28x%2B1%29%5E2%29-9%2F2\"$

\n" ); document.write( "The vertex is (-1,-9/2); the axis of symmetry is x=-1.

\n" ); document.write( "The y-intercept is where x=0; setting x=0 in the original form of the equation we see the y-intercept is (0,-4).

\n" ); document.write( "Then since the axis of symmetry is x = -1, the mirror of the y-intercept is (-2,-4).

\n" ); document.write( "To find the x-intercepts (the zeros of the function), the easiest way is to look at the original equation after the leading coefficient has been factored out:

\n" ); document.write( " $\"y+=+%281%2F2%29%28x%5E2%2B2x-8%29\"$
\n" ); document.write( " $\"y+=+%281%2F2%29%28x%2B4%29%28x-2%29\"$

\n" ); document.write( "The zeros are -4 and +2; the x-intercepts are (-4,0) and (2,0).

\n" ); document.write( " $\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%281%2F2%29x%5E2%2Bx-4%29\"$ \n" ); document.write( "

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