document.write( "Question 185073This question is from textbook college algebra concepts and models
\n" ); document.write( ": identify the vertex and the intercepts. F(x)= 1/4 (x^2 -16x +32), g(x)+ 1/2 (x^2 + 4x -2) \n" ); document.write( "
Algebra.Com's Answer #138837 by stanbon(75887)\"\" \"About 
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identify the vertex and the intercepts.
\n" ); document.write( "F(x)= 1/4 (x^2^ -16x +32),
\n" ); document.write( "(1/4)(x^2 -16x + ?) = y-8
\n" ); document.write( "(1/4)(x^2 - 16x + 64) = y-8+16
\n" ); document.write( "(1/4)(x-8)^2 = y+8
\n" ); document.write( "----------------------
\n" ); document.write( "Vertex: (8,-8)
\n" ); document.write( "intercepts:
\n" ); document.write( "x-intercept: Let y = 0 and solve for x:
\n" ); document.write( "(1/4)(x^2 - 16x + 32) = 0
\n" ); document.write( "x^2 -16x + 32 = 0
\n" ); document.write( "x = [16 +- sqrt(16^2 - 4*1*32)]/2
\n" ); document.write( "x = [16 +- sqrt(128)]/2
\n" ); document.write( "x = [16 +- 8sqrt(2)]/2
\n" ); document.write( "x = [8 +- 4sqrt(2)]
\n" ); document.write( "x = 8 + 4sqrt(2) or x = 8 - 4sqrt(2)
\n" ); document.write( "---
\n" ); document.write( "y-intercept:
\n" ); document.write( "Let x = 0 ; then y = (1/4)32 = 8
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\n" ); document.write( "\"graph%28400%2C300%2C-10%2C20%2C-10%2C10%2C%281%2F4%29%28x%5E2+-16x+%2B32%29%29\"
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\n" ); document.write( "\n" ); document.write( "g(x) = (1/2) (x^2^ + 4x -2)
\n" ); document.write( "(1/2)(x^2 + 4x +?) = y + 1
\n" ); document.write( "(1/2)(x^2 + 4x + 4) = y + 1 + 2
\n" ); document.write( "(1/2)(x+2)^2 = y + 3
\n" ); document.write( "----
\n" ); document.write( "Vertex:(-2,-3)
\n" ); document.write( "y-intercept:
\n" ); document.write( "Let x = 0, then y = (1/2)-2 = -1
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\n" ); document.write( "x-intercept
\n" ); document.write( "Let y=0, then (1/2)(x^2+4x-2) = 0
\n" ); document.write( "x^2 + 4x -2 = 0
\n" ); document.write( "x = [-4 +- sqrt(16 - 4*1*-2)]//2
\n" ); document.write( "x = [-4 +- sqrt(24)]/2
\n" ); document.write( "x = [-4 +- 2sqrt(6)]/2
\n" ); document.write( "x = [-2 +- sqrt(6)]
\n" ); document.write( "x = -2 + sqrt(6) or x = -2 - sqrt(6)
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\n" ); document.write( "\"graph%28400%2C300%2C-10%2C20%2C-10%2C10%2C%281%2F2%29%28x%5E2+%2B+4x+-2%29%29\"
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\n" ); document.write( "\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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