Answers to Assigned Problems in Lesson 03

  1. \( f(x) = (x-2)^2-3 \)
  2. \( f(x) = (x+1)^2+2 \)
  3. \( f(x) = (x-2)^2+7 \)
  4. \( f(x) = -2(x-2)^2+7 \)
  5. \( f(x) = \tfrac{1}{2}(x-3)^2 - 1 \)
  6. \( f(x) = -\tfrac{1}{4}(x+2)^2+3 \)
  7. Vertical: \( c = 12 \). Horizontal: \( \{ -3, -2 \} \)
  8. Vertical: \( c = -9 \). Horizontal: \( \{ -3, 1 \} \)
  9. Vertical: \( c = 4 \). Horizontal: \( \big\{ \frac{5\pm\sqrt{17}}{2} \big\} \)
  10. Vertical: \( c = 12 \). Horizontal: \( \big\{ \frac{-7\pm\sqrt{72}}{2} \big\} \)
  11. Vertical: \( c = -1 \). Horizontal: \( \big\{ \frac{3\pm\sqrt{5}}{4} \big\} \)
  12. Vertical: \( c = -15 \). Horizontal: \( \big\{ \frac{-1\pm\sqrt{34}}{2} \big\} \)