document.write( "Question 58493: Sketch the graph of f(x)=x^2-x-6 include all intercepts and the vertex \n" ); document.write( "
Algebra.Com's Answer #40124 by ankor@dixie-net.com(22740)\"\" \"About 
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f(x)=x^2-x-6
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\n" ); document.write( "\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-8%2C+8%2C+x%5E2+-+x+-+6%29+\"
\n" ); document.write( "f(x) = y
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\n" ); document.write( "y = x^2 - x - 6
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\n" ); document.write( "Factors to:
\n" ); document.write( "(x-3)(x+2) = 0
\n" ); document.write( "x = +3 and x = -2; (the x intercepts)
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\n" ); document.write( "y intercept when x = 0
\n" ); document.write( "y = 0^2 - 0 - 6
\n" ); document.write( "y = -6; (the y intercept)
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\n" ); document.write( "The vertex is the value of x when the parabola is at minimum
\n" ); document.write( "Can be found using the vertex equation: x = -b/(2a)
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\n" ); document.write( "In the form, ax^2 + bx + c, your equation: a = =1, b = -1, c = -6 (not used)
\n" ); document.write( "x = -b/(2a)
\n" ); document.write( "x = -(-1)/(2*1)
\n" ); document.write( "x = +1/2
\n" ); document.write( "x = .5 is the vertex, (as you can see by the graph)
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\n" ); document.write( "They did not ask what the minimum value (y) is but if you wanted to find it,
\n" ); document.write( "Substitute .5 for x in the original equation:
\n" ); document.write( "y = .5^2 - .5 - 6
\n" ); document.write( "y = .25 - .5 - 6
\n" ); document.write( "y = -6.25 is the minimum and occurs at the vertex, x = .5 (see graph)
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