https://file.aiquickdraw.com/mathbot/file/1727225183994zrrh9xrk.jpg

The given function is:

\[
f(x) = 2(x - 3)^2 + 4
\]

You are asked to rewrite it in the form \( f(x) = ax^2 + bx + c \).

### Steps to simplify:

1. Expand the squared term \( (x - 3)^2 \):

\[
(x - 3)^2 = x^2 - 6x + 9
\]

2. Substitute this back into the original function:

\[
f(x) = 2(x^2 - 6x + 9) + 4
\]

3. Distribute the \( 2 \) through the terms inside the parentheses:

\[
f(x) = 2x^2 - 12x + 18 + 4
\]

4. Combine like terms:

\[
f(x) = 2x^2 - 12x + 22
\]

So, the function in the form \( ax^2 + bx + c \) is:

\[
f(x) = 2x^2 - 12x + 22
\]

Would you like more details or have any further questions? Here are some related questions:

1. How do you expand \( (x - a)^2 \) in general?
2. What is the significance of completing the square in this context?
3. How would you factor \( 2x^2 - 12x + 22 \)?
4. How does the vertex form of a quadratic function relate to the standard form?
5. Can the same method be applied to other forms of quadratic functions?

**Tip:** Expanding squared binomials is essential when transforming between different forms of quadratic equations!

Rewrite the function f(x) = 2(x-3)^2 + 4 in the form f(x) = ax^2 + bx + c.

Explore the process of rewriting the quadratic function f(x) = 2(x-3)^2 + 4 into the standard form ax^2 + bx + c. Learn the steps of expanding and simplifying quadratic expressions using algebraic techniques suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation