document.write( "Question 769550: use the discriminant to determine the number of points of intersection on the line y= 3x +5 and the quadratic function f(x) = 3x^2 -2x-4
\n" ); document.write( "Solve to find the points of intersection. \n" ); document.write( "

Algebra.Com's Answer #468914 by josgarithmetic(39617) $\"\"$ $\"About$

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Finding points of intersection between the line and the parabola means we equate \"y\" and f(x):\r
\n" ); document.write( "\n" ); document.write( " $\"3x%2B5=3x%5E2-2x-4\"$
\n" ); document.write( "simplifying into $\"3x%5E2-2x-3x-4-5=0\"$
\n" ); document.write( " $\"3x%5E2-5x-9=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Finding how many points can use the discriminant of that:
\n" ); document.write( " $\"%28-5%29%5E2-4%2A3%2A%28-9%29\"$
\n" ); document.write( " $\"25%2B12%2A9\"$
\n" ); document.write( "...only need to see that this value is positive.
\n" ); document.write( "Seeing the discriminant is positive, means $\"3x%5E2-5x-9\"$ has TWO real roots, so this means TWO points of intersection between \"y\" and f(x). \n" ); document.write( "

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