Advanced MathVery hardGap between the x-coordinates of two intersections
Advanced Math practice question
The parabola y = x² − 4 and the line y = 2x + 4 meet at two points. What is the distance between the x-coordinates of those two points?
Answer: 6
Set equal: x² − 4 = 2x + 4, so x² − 2x − 8 = 0 and (x − 4)(x + 2) = 0. The x-coordinates are 4 and −2, which are 6 apart.
Common wrong answers
- If you answered 2
- 2 is the sum of the x-coordinates (4 + (−2)), not the distance between them.
- If you answered 4
- 4 is only the larger x-coordinate; the other is −2.
- If you answered -8
- −8 is the product of the x-coordinates.
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