document.write( "Question 201168This question is from textbook Intermediate algebra an applied approach
\n" ); document.write( ": Find the maximum or minimum value of f(x)= -3x^2 +4x-1 \n" ); document.write( "

Algebra.Com's Answer #151376 by Earlsdon(6294) $\"\"$ $\"About$

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Find the maximum/minimum of:
\n" ); document.write( " $\"f%28x%29+=+-3x%5E2%2B4x-1\"$ If you were to graph this quadratic equation, you would see that the resulting curve is a parabola that opens downward (also indicated by the negative coefficient of the first term), and this means that the vertex of the parabola will occur at the maximum point on the curve.
\n" ); document.write( "To find the value of the x-coordinate of this point, use:
\n" ); document.write( " $\"x+=+%28-b%29%2F2a\"$ where, for this equation, a = -3, and b = 4, so...
\n" ); document.write( " $\"x+=+%28-4%29%2F2%28-3%29\"$
\n" ); document.write( " $\"highlight%28x+=+2%2F3%29\"$ and to find the value of the y-coordinate, you just substitute $\"x+=+2%2F3\"$ into the given equation and solve for y (after replacing f(x) with y).
\n" ); document.write( " $\"y+=+%28-3%29x%5E2%2B4x-1\"$ Substitute $\"x+=+%282%2F3%29\"$
\n" ); document.write( " $\"y+=+-3%282%2F3%29%5E2%2B4%282%2F3%29-1\"$ Evaluate.
\n" ); document.write( " $\"y+=+-3%284%2F9%29%2B%288%2F3%29-1\"$
\n" ); document.write( " $\"y+=+-4%2F3%2B8%2F3-3%2F3\"$
\n" ); document.write( " $\"highlight%28y+=+1%2F3%29\"$ This is the value of the y-coordinate of the vertex (maximum).
\n" ); document.write( "The maximum point (the vertex) on the curve (a parabola) occurs at ( $\"2%2F3\"$ , $\"1%2F3\"$ )
\n" ); document.write( " $\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-3x%5E2%2B4x-1%29\"$ \n" ); document.write( "

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