Question

5

How does the graph of g(x)=9(x+9)2² change from the parent graph of f(x)=x²?
A It's wider and shifts 9 units right.
B It's wider and shifts 9 units up.
C It's narrower and shifts 9 units left.
D It's narrower and shifts 9 units down.

Answer 1

The graph of g(x) = 9(x+9)^2 is wider than the parent graph f(x) = x^2 and shifts 9 units to the left.

Step-by-step explanation:

The student is asking how the graph of g(x) = 9(x+9)^2 differs from the parent graph of f(x) = x^2.

To analyze the transformation, we compare each part of the function g(x) with the parent function.

The number 9 outside the parentheses affects the vertical stretch, making it wider if greater than 1 and narrower if less than 1.

Since 9 is greater than 1, the graph is wider.

The transformation (x+9) indicates a horizontal shift, not a vertical shift.

Having a positive number inside the parentheses with x actually moves the graph to the left by that number of units.

Therefore, the graph is wider and shifts 9 units left.