document.write( "Question 884576: what is the vertex of f(x) = x^2 -6x + 3 \n" ); document.write( "

Algebra.Com's Answer #534427 by Theo(13342) $\"\"$ $\"About$

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since the quadratic equation is in the standard form of ax^2 + bx + c = 0, you can determine the value of a, b, and c.
\n" ); document.write( "you get:
\n" ); document.write( "a = 1
\n" ); document.write( "b = -6
\n" ); document.write( "c = 3
\n" ); document.write( "the formula for the line of symmetry is x = -b/2a which becomes x = 6/2 which becomes 3.
\n" ); document.write( "the vertex has the coordinates of (-b/a2a, f(-b/2a)
\n" ); document.write( "to find f(-b/2a), you solve for f(3) to get f(3) = 3^2 - 6*3 + 3 which results in f(3) = 9 - 18 + 3 which results in f(3) = -6.
\n" ); document.write( "your vertex is at (3,-6)
\n" ); document.write( "the graph of your equation is shown below:
\n" ); document.write( " $\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cx%5E2+-+6x+%2B+3%29\"$
\n" ); document.write( "draw a vertical line at x = 3 and a horizontal line as y = -6 and the intersection of those lines will be the minimum point on the graph of y = x^2 - 6x + 3.
\n" ); document.write( "the vertex of a quadratic equation is either the minimum point on the graph or the maximum point on the graph.
\n" ); document.write( "for this graph, the vertex is the minimum point on the graph because the coefficient of the x^2 term is positive.\r
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