Advanced MathHardMinimum of a sum of two squared binomials
Advanced Math practice question
What is the minimum value of the function f(x) = (x − 3)² + (x + 1)²?
Answer: 8
Expand: 2x² − 4x + 10 = 2(x − 1)² + 8, which is least, 8, at x = 1. (Directly: f(1) = 4 + 4 = 8.)
Common wrong answers
- If you answered 0
- 0 would need both squares to be 0 at once, which is impossible.
- If you answered 1
- 1 is the x-coordinate of the minimum, not its value.
- If you answered 10
- 10 is f(0), not the 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.