Advanced MathHardDistance between the points where a horizontal line meets a parabola
Advanced Math practice question
In the xy-plane, the line y = 4 intersects the graph of y = x² − 5 at two points. What is the distance between those points?
Answer: 6
x² − 5 = 4 gives x² = 9, x = ±3. The points (3, 4) and (−3, 4) are 6 apart.
Common wrong answers
- If you answered 3
- 3 is one x-coordinate, half the distance.
- If you answered 4
- 4 is the shared y-coordinate.
- If you answered 9
- 9 is x², not a distance.
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.