Advanced MathHardTranslating a parabola so its vertex is at the origin
Advanced Math practice question
In the xy-plane, the graph of y = x² − 2x − 3 is translated so that its vertex lies at the origin. Which of the following is an equation of the translated graph?
- A. y = x²Correct
- B. y = (x − 1)² − 4
- C. y = x² + 4
- D. y = (x + 1)²
Answer: A. y = x²
The vertex of y = (x − 1)² − 4 is (1, −4). Moving it to (0, 0) removes both shifts, leaving y = x².
Why the other answers are wrong
- B. y = (x − 1)² − 4
- That is the original graph, with its vertex still at (1, −4).
- C. y = x² + 4
- y = x² + 4 has its vertex at (0, 4).
- D. y = (x + 1)²
- y = (x + 1)² has its vertex at (−1, 0).
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.