Advanced MathVery hardDistance between a parabola's zeros
Advanced Math practice question
The function f(x) = (x − 2)² − 9 has two zeros. What is the distance between them on the number line?
Answer: 6
Zeros satisfy (x − 2)² = 9, so x = 2 ± 3: at −1 and 5. The distance is 6.
Common wrong answers
- If you answered 3
- 3 is the half-width 2 − (−1); the zeros sit 3 on each side of x = 2, 6 apart.
- If you answered 4
- The vertex is at x = 2, but the zeros are 2 ± 3, spanning 6.
- If you answered 9
- 9 is the squared half-distance; the zeros are at −1 and 5.
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