Advanced Math practice question

Answer: 1

Set them equal: x² = 2x − 1, so x² − 2x + 1 = 0, which is (x − 1)² = 0. The single solution is x = 1. (The repeated root is what 'touches at exactly one point' means.)

Common wrong answers

If you answered 0

At x = 0 the parabola gives y = 0 and the line gives y = −1; they don't meet there.

If you answered 2

At x = 2 the parabola gives 4 and the line gives 3.

If you answered −1

−1 is the constant in the line's equation, not the x-coordinate of the touching point. Solving x² − 2x + 1 = 0 gives x = 1.

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