Advanced MathHardSquaring a binomial with a fraction
Advanced Math practice question
Which expression is equivalent to (x + 1/2)²?
- A. x² + x + 1/4Correct
- B. x² + 1/4
- C. x² + (1/2)x + 1/4
- D. x² + x + 1/2
Answer: A. x² + x + 1/4
(x + 1/2)² = x² + 2 · x · (1/2) + (1/2)² = x² + x + 1/4.
Why the other answers are wrong
- B. x² + 1/4
- The middle term is missing; 2 · x · (1/2) = x.
- C. x² + (1/2)x + 1/4
- The middle term is doubled: 2 · (1/2) = 1, so it is x, not (1/2)x.
- D. x² + x + 1/2
- The constant is (1/2)² = 1/4, not 1/2.
More Advanced Math questions
- Hard
A population of bacteria doubles every 3 hours. If it starts at 500, which function models the population P af… - Hard
How many real solutions does x² + 4x + 5 = 0 have? - Hard
A car worth $20,000 loses 15% of its value each year. What is its value after 2 years? - Hard
An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t ye… - Hard
If f(x) = x² − 1 and g(x) = x + 2, what is g(f(3))? - Hard
The parabola y = x² − 8x + 12 crosses the x-axis at two points. What is the x-coordinate of the vertex?
Not affiliated with the College Board. SAT is a trademark of the College Board.