Advanced MathHardSmaller intersection of a line and a parabola
Advanced Math practice question
In the xy-plane, the line y = 5x − 6 meets the parabola y = x² at two points. What is the smaller of the two x-coordinates of those points?
Answer: 2
Set x² = 5x − 6: x² − 5x + 6 = 0, so (x − 2)(x − 3) = 0. The x-coordinates are 2 and 3; the smaller is 2.
Common wrong answers
- If you answered 3
- 3 is the LARGER x-coordinate.
- If you answered 6
- 6 is the constant term, not an x-coordinate.
- If you answered -2
- −2 has the wrong sign; the factors give x = 2 and x = 3.
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.