Big Ideas Math Integrated III
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Big Ideas Math Integrated III View details
5. Transformations of Quadratic Functions
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Exercise 2 Page 73

Consider vertical translations, horizontal translations, and vertical stretches and shrinks.

Supposing that and are positive numbers, is a translation units right, vertical stretch or shrink with factor followed by a translation units up of the parent function See solution for negative values of or

Practice makes perfect

We want to determine how the constants and affect the graph of the quadratic function To do so, let's look at the possible transformations. Then we can more clearly identify the ones being applied to the parent function

Transformations of
Vertical Translations
Horizontal Translations
Vertical Stretch or Shrink
Reflections

Let's suppose that and are positive numbers. We conclude from the table that is a translation units right, vertical stretch or shrink with factor followed by a translation units up of the parent function What happens if or are negative?

  • If the horizontal translation is done to the left.
  • If the vertical translation is done downwards.
  • If after the stretch or shrink a reflection in the axis takes place.