16Hit1600
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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