document.write( "Question 70739: in y=ax^2+bx+c i understand that b is a strong determinant of the x-intercepts of the curve, but can you explain that more to me? and please give examples if possible! \n" ); document.write( "

Algebra.Com's Answer #50594 by josmiceli(19441) $\"\"$ $\"About$

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The roots, or x-intercepts, are found by the formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "rewrite this as
\n" ); document.write( " $\"x+=+%28-b+%2F+2a%29+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( "The $\"b%5E2+-+4ac\"$ under the square root sign
\n" ); document.write( "determines the nature of the x-intercepts (roots).
\n" ); document.write( "If $\"b%5E2+=+4ac\"$ , the whole 2nd term is zero, and
\n" ); document.write( "there is 1 x-intercept at $\"-b%2F%282a%29\"$ . All this
\n" ); document.write( "means is that the vertex of the parabola just kisses
\n" ); document.write( "the x-axis.
\n" ); document.write( "If $\"b%5E2+%3E+4ac\"$ , There are 2 x-intercepts at these locations:
\n" ); document.write( " $\"x+=+%28-b+%2F+2a%29+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=+%28-b+%2F+2a%29+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( "If $\"b%5E2+%3C+4ac\"$ , There are a pair of imaginary roots
\n" ); document.write( "(involving $\"sqrt%28-1%29\"$ )
\n" ); document.write( "All that means is that the parabola never touches the x-axis \n" ); document.write( "

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