Advanced MathHardVertical shift of a parabola
Advanced Math practice question
The function f is defined by f(x) = x² − 4, and the function g is defined by g(x) = f(x) + 3. What are the coordinates of the vertex of the graph of g?
- A. (0, −1)Correct
- B. (0, −4)
- C. (3, −4)
- D. (0, −7)
Answer: A. (0, −1)
The vertex of f is (0, −4). Adding 3 to f(x) moves every point of the graph up by 3, so the vertex becomes (0, −4 + 3) = (0, −1). (Directly: g(x) = x² − 1.)
Why the other answers are wrong
- B. (0, −4)
- (0, −4) is the vertex of f. The +3 shifts g's graph upward.
- C. (3, −4)
- Adding 3 to the OUTPUT shifts the graph vertically; it doesn't move the vertex sideways to x = 3.
- D. (0, −7)
- The 3 is added, not subtracted: −4 + 3 = −1.
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.