SAT Equivalent expressions Practice Question 18 (Hard)

Math · Advanced MathHard

The expression $4x^2 - 24x + 41$ is equivalent to $a(x - h)^2 + k$ , where $a$ , $h$ , and $k$ are constants. What is the value of $k$ ?

$-36$

$5$

$32$

$41$

Show answer and explanation

Answer: B

Factor 4 from the first two terms: $4(x^2 - 6x) + 41$ . Complete the square: $4(x^2 - 6x + 9) - 36 + 41 = 4(x - 3)^2 + 5$ . So $k = 5$ .

Choice C subtracts 9 instead of $4 \cdot 9 = 36$ , forgetting that the added 9 is multiplied by 4.

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