16Hit1600
Advanced MathMediumDistance between the x-intercepts of a parabola

Advanced Math practice question

The graph of f(x) = x² − 6x + 5 in the xy-plane has two x-intercepts. What is the distance between them?

Answer: 4

Factor: x² − 6x + 5 = (x − 1)(x − 5), so the x-intercepts are at x = 1 and x = 5. The distance between them is 5 − 1 = 4.

Common wrong answers

If you answered 3
3 is the x-coordinate of the vertex, halfway between the intercepts.
If you answered 5
5 is one intercept, not the gap between them.
If you answered 6
6 is the sum of the intercepts (and the axis of symmetry is at x = 3), not the distance.

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