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Using the quadratic parent function f(x) = x², match the following equations and transformations from the...

Using the quadratic parent function f(x) = x², match the following equations and transformations from the parent function.
g(x) = 4x²
g(x) = ¼x²
g(x) = x² + 4
g(x) = x² − 4
g(x) = (x − 4)²
g(x) = −x²
g(x) = (x + 4)²
1. reflection over x-axis
2. vertical stretch by factor of 4
3. vertical shrink by a factor of 1/4
4. right 4 units
5. left 4 units
6. up 4 units
7. down 4 units

Answer

  1. g(x) = 4x² → 2: Vertical stretch by a factor of 4.
  2. g(x) = ¼x² → 3: Vertical shrink by a factor of 1/4.
  3. g(x) = x² + 4 → 6: Shift up 4 units.
  4. g(x) = x² − 4 → 7: Shift down 4 units.
  5. g(x) = (x − 4)² → 4: Shift right 4 units.
  6. g(x) = −x² → 1: Reflection over the x-axis.
  7. g(x) = (x + 4)² → 5: Shift left 4 units.

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