Advanced MathHardVertex form: sum of the parameters
Advanced Math practice question
The expression 2x² − 12x + 23 can be written in the form 2(x − h)² + k, where h and k are constants. What is the value of h + k?
Answer: 8
Complete the square: 2x² − 12x + 23 = 2(x² − 6x) + 23 = 2(x − 3)² − 18 + 23 = 2(x − 3)² + 5. So h = 3, k = 5, and h + k = 8.
Common wrong answers
- If you answered 2
- 2 comes from h = 3, k = −1, forgetting to multiply the 9 by 2 when completing the square.
- If you answered 26
- 26 comes from k = 23, not subtracting 2 × 9.
- If you answered -3
- −3 uses h = −3, the wrong sign from (x − h).
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