Which Equation Is The Inverse Of $y = 2x^2 - 8$?A. $y = \pm \sqrt{\frac{x+8}{2}}$B. \$y = \frac{\pm \sqrt{x+8}}{2}$[/tex\]C. $y = \pm \sqrt{\frac{x}{2} + 8}$D. $y = \frac{\pm \sqrt{x}}{2} + 4$

=====================================================

Introduction

In mathematics, an inverse function is a function that reverses the operation of another function. In other words, if we have a function f(x) and its inverse f^(-1)(x), then f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. In this article, we will focus on finding the inverse of a quadratic equation.

What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (usually x) is two. The general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants, and a cannot be zero.

The Given Equation

The given equation is:

y = 2x^2 - 8

This is a quadratic equation in the form of y = ax^2 + bx + c, where a = 2, b = 0, and c = -8.

Finding the Inverse

To find the inverse of a quadratic equation, we need to swap the variables x and y and then solve for y. Let's start by swapping the variables:

x = 2y^2 - 8

Solving for y

Now, we need to solve for y. To do this, we can start by adding 8 to both sides of the equation:

x + 8 = 2y^2

Dividing by 2

Next, we can divide both sides of the equation by 2:

(x + 8) / 2 = y^2

Taking the Square Root

Since y^2 is a perfect square, we can take the square root of both sides of the equation:

y = ±√((x + 8) / 2)

Simplifying the Expression

We can simplify the expression by removing the parentheses:

y = ±√(x + 8) / 2

Comparing with the Options

Now, let's compare our result with the options:

A. y = ±√(x + 8) / 2 B. y = ±√(x + 8) / 2 C. y = ±√(x / 2 + 8) D. y = ±√(x) / 2 + 4

Conclusion

Based on our calculation, the correct answer is:

A. y = ±√(x + 8) / 2

This is the inverse of the given quadratic equation y = 2x^2 - 8.

Final Answer

The final answer is A.