Advanced MathHardWhere a downward parabola is non-negative
Advanced Math practice question
The function g is defined by g(x) = −(x + 3)² + 4. For which values of x is g(x) ≥ 0?
- A. −5 ≤ x ≤ −1Correct
- B. x ≤ −5 or x ≥ −1
- C. x ≥ −3
- D. All real x
Answer: A. −5 ≤ x ≤ −1
g(x) = 0 when (x + 3)² = 4, i.e. x = −1 or −5. The parabola opens downward, so g ≥ 0 between them.
Why the other answers are wrong
- B. x ≤ −5 or x ≥ −1
- Outside the zeros the parabola is negative.
- C. x ≥ −3
- x ≥ −3 runs past x = −1, where g turns negative.
- D. All real x
- g(0) = −5, so not all x.
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.