Advanced MathHardSystem with a quadratic: number of solutions
Advanced Math practice question
How many solutions does the system y = x² + 1 and y = 1 − x² have?
- A. Exactly oneCorrect
- B. Exactly two
- C. None
- D. Infinitely many
Answer: A. Exactly one
Set equal: x² + 1 = 1 − x², so 2x² = 0 and x = 0 only. The parabolas touch at (0, 1).
Why the other answers are wrong
- B. Exactly two
- Two would need two distinct x-values; 2x² = 0 has just x = 0.
- C. None
- (0, 1) satisfies both.
- D. Infinitely many
- Two different parabolas can't coincide.
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