Question

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).

Answer 1

See below

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