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Roger has the graph of F(x)=-4x^2 but needs to sketch the graph of G(x)=(x+3)^2 + 2/3. Describe how Roger can use the graph of F(x) to sketch the graph of G(x).

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mhanifa

Answer:

See below

Step-by-step explanation:

Given

  • Parent function f(x)= -4x^2
  • Transformed function g(x) = (x+3)^2 + 2/3

We need to describe the transformations from f to g

The transformation steps are:

  • f(x) = -4x^2 → 4x^2 → x^2 → (x+3)^2 → (x+3)^2 + 2/3 = g(x)

So there are four transformations:

  • Reflect over x-axis
  • Stretch horizontally by a factor of 4
  • Translate left by 3 units
  • Translate up by 2/3 units

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