https://file.aiquickdraw.com/mathbot/file/1728743753730oakzmkwb.jpg

The equation provided in the image is:

\[
2(x + 2)^2 = y - 2
\]

Let's solve for \(y\) in terms of \(x\).

### Step-by-Step Solution:
1. Start with the given equation:
   \[
   2(x + 2)^2 = y - 2
   \]
   
2. Add 2 to both sides to isolate \(y\):
   \[
   2(x + 2)^2 + 2 = y
   \]

3. The equation for \(y\) is now:
   \[
   y = 2(x + 2)^2 + 2
   \]

This is the solution for \(y\) in terms of \(x\).

Would you like further details or clarifications on any step? Feel free to ask!

Here are 5 related questions you might want to explore:
1. How do you graph the function \(y = 2(x + 2)^2 + 2\)?
2. What is the vertex of the parabola represented by \(y = 2(x + 2)^2 + 2\)?
3. How does the factor of 2 affect the shape of the parabola compared to \(y = (x + 2)^2\)?
4. Can you find the axis of symmetry for the quadratic function?
5. How would you rewrite \(y = 2(x + 2)^2 + 2\) in standard form?

**Tip:** When solving equations involving squares, always remember to check for any additional solutions when you square both sides!

Learn how to solve the equation 2(x + 2)^2 = y - 2 for y in terms of x with a step-by-step solution. This problem involves key algebraic concepts such as quadratic equations, equation-solving techniques, and properties of parabolas. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation