document.write( "Question 617716: Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis.\r
\n" ); document.write( "\n" ); document.write( "y = 2x2 + x - 3
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #388505 by Theo(13342)\"\" \"About 
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your equation is:
\n" ); document.write( "y = 2x^2 + x - 3
\n" ); document.write( "set the equation equal to 0 and factor it.
\n" ); document.write( "the equation becomes:
\n" ); document.write( "2x^2 + x - 3 = 0
\n" ); document.write( "the factors of this equation are:
\n" ); document.write( "(2x + 3) * (x - 1) = 0
\n" ); document.write( "the roos of this equation are:
\n" ); document.write( "x = -3/2 and x = 1
\n" ); document.write( "those are the intersection of the graph of the equation with the x-axis.
\n" ); document.write( "the vertex of the equation must lie below the x-axis.
\n" ); document.write( "to confirm that, use the formula for the line of symmetry to find the vertex.
\n" ); document.write( "the standard form of a quadratic equation is equal to:
\n" ); document.write( "ax^2 + bx + c = 0
\n" ); document.write( "in your equation, that makes:
\n" ); document.write( "a = 2
\n" ); document.write( "b = 1
\n" ); document.write( "c = -3
\n" ); document.write( "the formula for the line of symmetry, which is also the x value of the vertex, is:
\n" ); document.write( "x = -b/2a
\n" ); document.write( "that becomes -1/4.
\n" ); document.write( "when x is equal to -1/4, y is equal to 2*(-1/4)^2 + (-1/4) - 3 which becomes:
\n" ); document.write( "1/8 - 1/4 - 3 which is equal to -3.125
\n" ); document.write( "that makes the vertex equal to (-1/4, -3.125)
\n" ); document.write( "the graph of this equation looks like this:
\n" ); document.write( "\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C2x%5E2+%2B+x+-+3%29\"\r
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