Advanced MathMediumExpanding a scaled squared binomial
Advanced Math practice question
Which expression is equivalent to 2(x − 3)² + 5?
- A. 2x² − 12x + 23Correct
- B. 2x² − 6x + 14
- C. 2x² + 23
- D. 2x² − 12x + 14
Answer: A. 2x² − 12x + 23
(x − 3)² = x² − 6x + 9, so 2(x − 3)² + 5 = 2x² − 12x + 18 + 5.
Why the other answers are wrong
- B. 2x² − 6x + 14
- This doubles only the x² term.
- C. 2x² + 23
- This drops the middle term.
- D. 2x² − 12x + 14
- This forgets to double the 9 before adding 5.
More Advanced Math questions
- Medium
What are the solutions to x² − 5x + 6 = 0? - Medium
The graph of f(x) = (x − 3)² + 4 is a parabola. What are the coordinates of its vertex? - Medium
If x² − 2x − 8 = (x + 2)(x − a), what is the value of a? - Medium
If √(x + 5) = 4, what is the value of x? - Medium
If f(x) = x + 3 and g(x) = 2x, what is f(g(4))? - Medium
What are the solutions to x² + 6x + 8 = 0?
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