Advanced MathMediumSecond input from two points on a parabola through the origin
Advanced Math practice question
In the xy-plane, the graph of y = ax² passes through the points (2, 12) and (k, 27), where a and k are positive constants. What is the value of k?
Answer: 3
From (2, 12): 4a = 12, a = 3. Then 3k² = 27 → k² = 9 → k = 3.
Common wrong answers
- If you answered 9
- 9 is k², before taking the square root.
- If you answered 4.5
- 4.5 scales 2 by 27/12, treating the relationship as linear.
- If you answered -3
- −3 is ruled out by k > 0.
More Advanced Math questions
- Medium
What are the solutions to x² − 5x + 6 = 0? - Medium
The graph of f(x) = (x − 3)² + 4 is a parabola. What are the coordinates of its vertex? - Medium
If x² − 2x − 8 = (x + 2)(x − a), what is the value of a? - Medium
If √(x + 5) = 4, what is the value of x? - Medium
If f(x) = x + 3 and g(x) = 2x, what is f(g(4))? - Medium
What are the solutions to x² + 6x + 8 = 0?
Not affiliated with the College Board. SAT is a trademark of the College Board.