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2005 AMC 12B Question 8

AMC12 · 2005 AMC 12B

Question 8

For how many values of $a$ is it true that the line $y = x + a$ passes through the vertex of the parabola $y = x^2 + a^2?$
  1. $0$
  2. $1$
  3. $2$
  4. $10$
  5. infinitely many