Advanced MathHardNumber of intersection points
Advanced Math practice question
How many points do the graphs of y = x² and y = 4x − 4 have in common?
- A. Exactly oneCorrect
- B. Exactly two
- C. None
- D. Infinitely many
Answer: A. Exactly one
x² = 4x − 4 gives (x − 2)² = 0: one repeated solution, x = 2. The line is tangent to the parabola at (2, 4).
Why the other answers are wrong
- B. Exactly two
- Two would need two distinct roots; the discriminant 16 − 16 = 0 gives one.
- C. None
- (2, 4) is on both.
- D. Infinitely many
- A line and a parabola can't coincide.
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