Advanced MathMediumCounting distinct x-intercepts
Advanced Math practice question
The function f is defined by f(x) = (x − 2)²(x + 1). At how many distinct points does the graph of f cross or touch the x-axis?
Answer: 2
f(x) = 0 when x − 2 = 0 or x + 1 = 0, so at x = 2 (a repeated factor, where the graph touches) and x = −1 (where it crosses). Two distinct points.
Common wrong answers
- If you answered 0
- The graph does meet the x-axis, at x = 2 and x = −1.
- If you answered 1
- 1 misses x = −1, which is also a zero.
- If you answered 3
- 3 counts the repeated factor (x − 2) twice, but it gives the same point, x = 2.
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