document.write( "Question 292007: What is the maximum point of the function $\"+f%28x%29=-3x%5E2%2B24x-30+\"$ ?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #211038 by nerdybill(7384) $\"\"$ $\"About$

You can put this solution on YOUR website!
What is the maximum point of the function $\"+f%28x%29=-3x%5E2%2B24x-30+\"$ ?
\n" ); document.write( ".
\n" ); document.write( "Since the given equation is a parabola that opens downward (we know this from the coefficient associated with the x^2 term -- if it is negative it opens downward -- if it is positive it opens upward). The vertex will give you the maximum.
\n" ); document.write( ".
\n" ); document.write( "There are a few ways to find the vertex.
\n" ); document.write( "One way is to find the \"axis of symmetry\":
\n" ); document.write( "x = -b/2a = -24/(2(-3)) = -24/-6 = 4
\n" ); document.write( "That's the x-coordinate.
\n" ); document.write( ".
\n" ); document.write( "To find the y-coordinate, plug it in back to the original function:
\n" ); document.write( "f(x)=-3x^2+24x-30
\n" ); document.write( "f(4)=-3(4)^2+24(4)-30
\n" ); document.write( "f(4)=-48+96-30
\n" ); document.write( "f(4)=18
\n" ); document.write( ".
\n" ); document.write( "Maximum point is at (4,18)
\n" ); document.write( " \n" ); document.write( "

\n" );