Question

Use the given parent function to answer the question.

Information
f of x equals x squared

Question
Which graph represents the function f of left-parenthesis x plus 3 right-parenthesis?

Answer options with 4 options
A.
On a coordinate plane, an upward opening parabola has a vertex at (3, 0).

C.
On a coordinate plane, an upward opening parabola has a vertex at (negative 3, 0).

B.
On a coordinate plane, an upward opening parabola has a vertex at (0, negative 3).

D.
On a coordinate plane, an upward opening parabola has a vertex at (0, 3).

Answer 1

The parent function given is \( f(x) = x^2 \).

To determine the graph that represents the function \( f(x + 3) \), we need to understand how the transformation works. The expression \( f(x + 3) \) represents a horizontal shift to the left by 3 units.

Since the vertex of the original parent function \( f(x) = x^2 \) is at (0, 0), shifting this vertex left by 3 units will move it to the point (-3, 0).

So the graph of \( f(x + 3) \) will be an upward opening parabola with its vertex at (-3, 0).

The correct answer, therefore, is:

**C. On a coordinate plane, an upward opening parabola has a vertex at (negative 3, 0).**