Rules

Transformations of one polynomial function were discussed in the quadratic unit. To translate the graph of a quadratic function, we can use the vertex form of a quadratic function, f(x) = a(x - h)2 + k. The transformations followed these rules:

  • f (x) + k is f(x) shifted upward k units
  • f (x) - k is f(x) shifted downward k units
  • f (x + h) is f(x) shifted left h units
  • f (x - h) is f(x) shifted right h units
  • -f(x) is f(x) flipped upside down ("reflected about the x-axis")
  • f (-x) is the mirror of f(x) ("reflected about the y-axis")
  • af(x) stretches the graph vertically if a > 1
  • af(x) shrinks the graph vertically if 0 < a < 1
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