Advanced Math practice question

Answer: A. Zero

Set them equal: x² + 1 = x, so x² − x + 1 = 0. The discriminant is (−1)² − 4(1)(1) = −3, which is negative, so there are no real solutions — the graphs never meet. (The parabola's lowest point is (0, 1), which already sits above the line there.)

Why the other answers are wrong

B. Exactly one

Exactly one point would need a discriminant of zero; here it's −3.

C. Exactly two

Two points would need a positive discriminant. −3 is negative.

D. Infinitely many

A line and a parabola can share at most two points; infinitely many is impossible.

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