Problem

Convert \(f(x)=3x^{2}+12x+8\) to vertex form. Factor \(3\) from the \(x\)-terms, complete the square inside, distribute the compensation correctly, state the vertex, and verify with expansion and the displayed graph.

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factoring=3(x²+4x)+8; half=2; square=4; completion=3(x²+4x+4)+8; vertex form=3(x+2)²+8; vertex=(-2,8); expansion check=3x²+12x+20

factoring=left 3 inside; half coefficient=6; square=36; completion=3x²+12x+36−36+8; vertex form=3(x+2)²−28; vertex=(-2,-28); expansion check=3x²+12x−16

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

Factor 3(x² + 4x) + 8; half inside 2 and square 4; completion 3[(x − 2)² − 4] + 8; vertex form 3(x − 2)² − 4; vertex (2, −4); expansion 3x² − 12x + 8.

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Convert \(f(x)=3x^{2}+12x+8\) to vertex form. Factor \(3\) from the \(x\)-terms, complete the square inside, distribute the compensation correctly, state the vertex, and verify with expansion and the displayed graph.

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