document.write( "Question 7124: Find the vertex and intercepts for the quadratic function y=x^2+x-6. Sketch the graph, and state the domain and range. Any help is greatly appreciated. \n" ); document.write( "

Algebra.Com's Answer #3913 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find the x-intercepts (the zeros), set the quadratic = 0 and solve for x:
\n" ); document.write( " $\"x%5E2+%2B+x+-+6+=+0\"$ Factor.
\n" ); document.write( " $\"%28x+%2B+3%29%28x+-+2%29+=+0\"$ Apply the zero product principle.
\n" ); document.write( " $\"x+%2B+3+=+0\"$ , $\"x+=+-3\"$
\n" ); document.write( " $\"x+-+2+=+0\"$ , $\"x+=++2\"$ \r
\n" ); document.write( "\n" ); document.write( "The x-intercepts are: (-3, 0) and (2, 0)\r
\n" ); document.write( "\n" ); document.write( "The x-coordinate of the vertex is at: -b/2a = -1/2. (ax^2 + bx + c = 0)Substitute this into the quadratic equation and solve for the y-coordinate.
\n" ); document.write( " $\"y+=+%28-1%2F2%29%5E2+%2B+%28-1%2F2%29+-+6\"$
\n" ); document.write( " $\"y+=+1%2F4+-+1%2F2+-+6\"$
\n" ); document.write( " $\"y+=+-26%2F4\"$ = - 6 1/4\r
\n" ); document.write( "\n" ); document.write( "The vertex is at: (-1/2, -6 1/4)\r
\n" ); document.write( "\n" ); document.write( "The graph of this quadratic equationis:
\n" ); document.write( " $\"graph%28300%2C200%2C-5%2C5%2C-7%2C10%2Cx%5E2%2Bx-6%29\"$ \r
\n" ); document.write( "\n" ); document.write( "The domain (the set all possible values of the independent variable, that's x) is the set of all real numbers.
\n" ); document.write( "The range (the set of all possible values of the dependent variable, that's y) is also the set of all real numbers. \n" ); document.write( "

\n" );