Problem

Rewrite \(f(x)=2x^{2}-8x+3\) in vertex form. Factor \(2\) from the variable terms before completing the square, apply that factor to the compensation, identify the vertex, and expand to check.

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factor leading coefficient=2(x²−4x)+3; half inside coefficient=-2; square added inside=4; completion=2[(x−2)²−4]+3; vertex form=f(x)=2(x−2)²−5; vertex=(-2,-5); expansion check=2(x−2)²−5=2x²−8x+3

factor leading coefficient=2(x²−4x)+3; half inside coefficient=-2; square added inside=4; completion=2[(x−2)²−4]+3; vertex form=f(x)=2(x−2)²−5; vertex=(2,-5); expansion check=2(x−2)²−5=2x²−8x+3

leading coefficient not factored; half coefficient=-4; square added=16; completion=x²−8x+16−16+3; vertex form=f(x)=(x−4)²−13; vertex=(4,-13); expansion check=(x−4)²−13=x²−8x+3

factor leading coefficient=2(x²−4x)+3; half inside coefficient=-2; square added inside=4; completion=2(x−2)²−4+3; vertex form=f(x)=2(x−2)²−1; vertex=(2,-1); expansion check=2(x−2)²−1=2x²−8x+7

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Rewrite \(f(x)=2x^{2}-8x+3\) in vertex form. Factor \(2\) from the variable terms before completing the square, apply that factor to the compensation, identify the vertex, and expand to check.

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