document.write( "Question 180347This question is from textbook algebra structure and method
\n" ); document.write( ": can you please help me solve the following: (((How many x-intercepts the parabola has and wheather its vertex lies above or below or on the x-axis, y=x^2-5x+6))) \n" ); document.write( "

Algebra.Com's Answer #135209 by Mathtut(3670) $\"\"$ $\"About$

You can put this solution on YOUR website!
set y = to zero when trying to find the x intercepts
\n" ); document.write( ":
\n" ); document.write( " $\"x%5E2-5x%2B6=0\"$
\n" ); document.write( ":
\n" ); document.write( " $\"%28x-2%29%28x-3%29=0\"$
\n" ); document.write( ":
\n" ); document.write( "x=2 and 3
\n" ); document.write( ":
\n" ); document.write( "since this has two intercepts we know that the vertex is NOT on the x axis
\n" ); document.write( ":
\n" ); document.write( "we also know that this parabola opens up(coefficent is positive in x squared term) therefore we know the vertex is below the x axis, but not by much because the x intercepts are very close to each other
\n" ); document.write( ":
\n" ); document.write( "we can find the exact vertex by completing the square
\n" ); document.write( ":
\n" ); document.write( " $\"y=x%5E2-5x%2B%2825%2F4%29%296-25%2F4\"$
\n" ); document.write( ":
\n" ); document.write( " $\"y=%28x-%285%2F2%29%29%5E2-%281%2F4%29\"$
\n" ); document.write( ":
\n" ); document.write( "so the vertex is at (5/2,-1/4)
\n" ); document.write( ":
\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-5x%2B6%29\"$ \n" ); document.write( "

\n" );