document.write( "Question 173956: This is one main question with several parts. Please help. Thank you,
\n" ); document.write( "How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. \n" ); document.write( "

Algebra.Com's Answer #128849 by vleith(2983) $\"\"$ $\"About$

You can put this solution on YOUR website!
1) Look at the value of the discrimenent. Then you can see if there are 0, 1 or 2
\n" ); document.write( "2) If you are given roots, then you can 'recreate' the eqaution as follows
\n" ); document.write( "y = (x - X1)(x - X2) sub in the roots for X1 and X2, then expand the equation
\n" ); document.write( "3) Sure, imagine a parabola that intersects the x axis in two places. Now imagine a different parabola, with the same two intercepts but a more or less steep curve and a vertex higher of lower.\r
\n" ); document.write( "\n" ); document.write( "Easier to draw it than describe it.
\n" ); document.write( "Layout a coordinate plane
\n" ); document.write( "Pick two points on the x axis
\n" ); document.write( "pick a vertex below the x axis
\n" ); document.write( "Draw the parabola that connects all three of those points.
\n" ); document.write( "Now, move the vertex point twice as far below the x axis as the first vertex.
\n" ); document.write( "Now, draw the parabola that contains the new vertex and the 2 roots on the x axis.\r
\n" ); document.write( "\n" ); document.write( "Now ou see two different curves with the same roots. \n" ); document.write( "

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