Complete the square for \(3x^{2}-18x+4\). Extract the leading coefficient from the \(x\text{-}\text{terms}\), form the inner binomial square, account for the outer factor in the constant correction, and give the vertex.

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3(x − 3)² − 9 + 4 = 3(x − 3)² − 5. The subtraction of 9 must be multiplied by 3.

3(x² − 6x + 4) = 3[(x − 3)² − 5]. This incorrectly moves the constant 4 inside the factor 3.

3x² − 18x + 4 = 3(x² − 6x) + 4 = 3[(x − 3)² − 9] + 4 = 3(x − 3)² − 23. The vertex is (3, −23).

(x − 3)² − 5 has vertex (3, −5). This omits the leading factor 3.

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Curriculum context

Course: Math II
Standard: A-SSE.3.b
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Complete the square to reveal maximum or minimum values of quadratic functions.
Problem type: Complete the square for a nonmonic quadratic