document.write( "Question 202262: Find the vertex of f(x) = x^2-10x+21. Is the vertex the maximum or minimum value of f? How do you know? \n" ); document.write( "

Algebra.Com's Answer #152515 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the vertex of:
\n" ); document.write( " $\"f%28x%29+=+x%5E2-10x%2B21\"$
\n" ); document.write( "The x-coordinate of the vertex is given by:
\n" ); document.write( " $\"x+=+%28-b%29%2F2a\"$ and in this problem, a = 1, b = -10, so...
\n" ); document.write( " $\"x+=+-%28-10%29%2F2%281%29\"$
\n" ); document.write( " $\"x+=+5\"$ To find the y-coordinate, substitute this into the given quadratic equation and solve for y (f(x)).
\n" ); document.write( " $\"y+=+x%5E2-10x%2B21\"$ Substitute x = 5.
\n" ); document.write( " $\"y+=+5%5E2-10%285%29%2B21\"$ Evaluate.
\n" ); document.write( " $\"y+=+25-50%2B21\"$
\n" ); document.write( " $\"y+=+-4\"$
\n" ); document.write( "The vertex is at (5, -4)
\n" ); document.write( "This is a minimum point on the curve because the positive value of the $\"x%5E2\"$ coefficient indicates that the parabola opens upwards.
\n" ); document.write( " $\"graph%28400%2C400%2C-5%2C10%2C-5%2C5%2Cx%5E2-10x%2B21%29\"$ \n" ); document.write( "

\n" );