The function g is related to one of the parent functions described in an earlier section.
g(x) = x2 + 6
(a) Identify the parent function f.

The given function is:

\[
g(x) = x^2 + 6
\]

This function resembles the **parent function** of the quadratic family, which is:

\[
f(x) = x^2
\]

The parent function \( f(x) = x^2 \) is a basic quadratic function, which is a parabola with its vertex at the origin (0, 0). 

In the function \( g(x) = x^2 + 6 \), the graph of \( f(x) = x^2 \) is shifted **upward by 6 units** due to the "+6" constant. This is a vertical translation.

**Answer:**
The parent function is \( f(x) = x^2 \).

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Would you like a more detailed explanation of how this shift works? Or do you have any other questions? Here's a list of related topics you might find helpful:

1. What is the effect of vertical translations on a function?
2. How do you graph quadratic functions?
3. What are the characteristics of a parent quadratic function?
4. How does a transformation of functions impact the graph?
5. What is the general form of a quadratic function?

**Tip:** Always look for constants added to the function to identify vertical translations in transformations.

The function g is related to one of the parent functions described in an earlier section. g(x) = x^2 + 6 (a) Identify the parent function f.

Discover how to identify the parent function of g(x) = x^2 + 6. Learn about quadratic functions, transformations, and vertical translations. This step-by-step explanation is ideal for students in Grades 8-10.

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