Advanced MathHardMinimum and axis from vertex form with a coefficient
Advanced Math practice question
The function r is defined by r(x) = 3(x − 2)² + 1. Which statement is true?
- A. The minimum value of r is 1, at x = 2.Correct
- B. The minimum value of r is 3, at x = 2.
- C. The minimum value of r is 1, at x = −2.
- D. The maximum value of r is 1, at x = 2.
Answer: A. The minimum value of r is 1, at x = 2.
3(x − 2)² ≥ 0 with equality at x = 2, so the minimum is 1 there.
Why the other answers are wrong
- B. The minimum value of r is 3, at x = 2.
- 3 is the leading coefficient, not the minimum.
- C. The minimum value of r is 1, at x = −2.
- (x − 2)² is zero at x = 2, not −2.
- D. The maximum value of r is 1, at x = 2.
- The coefficient 3 is positive, so the vertex is a minimum.
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.